No Support

This is the most typical issue-the mom wants to homeschool, the dad is skeptical. Or the grandparents start flapping around making noises. Or the neighbors. The issue of 'other people'.
First things first-look at yourself before you start trying to figure out why everyone else is against the idea.
How often have you started a project-totally gung-ho about it-and then dropped it days or weeks later?
Do you often complain of not being able to take care of 'everything' around the house?
How often have you called your husband at work over some minor crisis?
Is your flowerbed weeded? Yard mowed?
Are you always late?
Do you cringe at the thought of someone seeing what your house looks like more than 75% of the time?

No one is perfect, everyone has big ideas that turn cold or they fall apart now and then. But these are your children, their very future depends on the foundation they will spend their entire childhood building. You need to be able to run your household, to take care of things that pop up, to be able to handle the day-to-day process of being with your children around the clock. It's not like school at home. You still have to run errands and make beds and get the dog to the vet, but you also have to be sure each child has their needs met for the day, has been allowed to explore and learn, that they have had time with just you-real face time and not you going 'uh-huh' as you type a quick e-mail or fold some towels.

So let's look at this.

How available are you right for your kids now?
Homeschooling is filled with adventures and days spent making things and being on the go. But you have to plan the adventures, what gets made has to be prepared for and cleaned up afterward, stored somewhere and when you go and go, you still have to be able to meet your other needs-your home and errands, possibly a job as well. And your husband does not want you too tired or stressed to give him some attention, he does not want you calling him because Junior won't do his math work, he does not want to come home to piles of laundry and you laying down to rest because being with the kids all day is just so hard.
I may sound like I am straight out of the 1950's, but face it. In situations like this one-"My husband will not let me homeschool!" generally one of two things is going on. Either he was so enamored with his school career he can't bear the thought of his child not having exactly the same experience (or else he had a horrible go and wants to try again via your kid) or else he has misgivings about your ability to actually keep up and provide your children with a comparable or better education than they could get in public school. Your background as a 'housewife' will have a large bearing on his enthusiasm.
If this is not the issue, if you really are on the ball and usually have things well under control, then ask him what his concerns are. He may think only religious fanatics homeschool or that it will cost mega bucks. He may worry what people will think, he may be concerned it will be too much when things seem to be going so well now.
Do what you can to put his mind at ease. Come up with a timeline for pulling them out of school or starting to introduce very simple lessons if they are still little yet. Work out a way he can be comfortable, but do not put yourself and your kids through a 'trial run' where you 'just see' how things go. If you pull your kids out of public school, they will need months, even a whole year, to deschool and learn how to be curious again without someone deciding for them how their day will be divided up.
Pulling them out to 'school at home' will be horrible for all of you. You will be stressed to show results, they will not have a chance to enjoy their new freedom and it will go badly.
If your husband just can not support you and the children you share, then it's time for you to do some real thinking about where you see things going.

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Many families settle right in, both parents are delighted to be able to homeschool, Dad could care less that his socks are all being systematically turned into puppets to reenact King Lear and the kids are using the mold around the tub as science class. Mom is easy-going and the kids are loving the freedom. When, along comes Grand. Grand likes to stick his/her nose in because Grand has been there and done that and so therefore knows better than Mom and Dad.
Grand may have nothing to do with day-to-day life and in fact may actually live some distance away. Mom and Dad may owe Grand money or otherwise feel obligated to bear the guilt of "keeping those kids from a proper education".
The thing is, Grand had their shot. Mom and Dad need to sit down and come up with the family front, because Grand will chip from any angle. Little questions about what the kids learned today, over-reactions to math inaccuracies, clucking like sad chickens over spelling errors. These are all undermining Mom and Dad the same way Grand giving the kids cookies before dinner or picking up their toys for them is undermining. It must be squelched and you don't have to be nice. They are playing dirty when they start bringing the kids into the battle, especially if their sole reason is to see what mistakes the kids make with answers.
You simply must stand your ground, distance yourself, ignore what you can and set firm limits on interaction. You may have to train your kids to be rude in ways like blowing off 'quizzes', saying things like, "How come you never ask what I learned today when public schools are out?" Or "Well what did YOU learn today?"
You don't have a dog and pony show, you have kids. Goodie, your sister's children are on the honor roll. That means they can memorize and regurgitate. Things your kids (and everyone else's) accomplished at birth-they oogled your face and spit up regularly (the two are not connected...probably). Her kids can play the system-that's great! They will make excellent employees. Your brother's kid is in band-too bad homeschoolers are forbidden to take music lessons. Oh, wait.
You don't have their kids, you have yours. Chances are pretty good your nieces and nephews annoy the socks off of you, or are total strangers. The reason for this is---you did not listen to your parents while you were growing up and you turned out wrong! This is excellent news because it means you can just keep on doing it now. Refuse all temptation to show them up and don't give in to demands of testing or any other crap like that, either. They don't have your child's best interest at heart, they have their own agenda.
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Nosy neighbors, fickle friends.
Neighbors will be at work all day, fences are good investments. Moving should always be an option.
As for friends-there are MILLIONS of people out there, get new ones.
Seriously, don't let people interfere with raising your children. If they don't have a legitimate reason-and I doubt they do-then ditch them. You can legally shoot trespassers. You can get caller ID and delete e-mails. You don't have to interact with anyone who does not lift your spirits. I suggest a serious culling of those around you if you are not getting the support you need.  The homeschooling community is vast.  It may take a year or two or you may meet your new best friend on your first outing.  

These are the people you need in your life and they are worth the time it takes to find them.

And you won't get to keep them all, but the one or two who come through it with you are worth their weight in gold.

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First and always, look at yourself before you respond in any of these situations-especially before you throw a hissy fit. Don't give them more reasons to be against you. Ask yourself "How often do I quit?" "What sort of advantages can I offer my kids by keeping them home?" "How do I handle stress?"

Then ask the doubter, "Why do you feel I am incapable?" "Would you be willing to help where I need it most?" "Can you explain your feelings and reservations?"

Don't go on the attack, don't be more rude than is called for and don't put up with anything you feel is unfair. State your reasons, stand your ground and be ready to back yourself up with actions. This does not mean posting the kids test scores, this means keeping things running, getting out and making connections in the community, providing for and expanding your children's talents and using the freedom of homeschooling to travel and learn together. Be active. Be seen.

What can anyone say then? :

She homeschools and her kids are always busy doing things?

They took the kids out of school and are traveling?
Their kid built a life-size dinosaur out of paper mache?
That family is constantly doing things together?
Those kids sleep late?
What is the worst they can come up with?