Just time for a quick post on our experiences with this...
My mom was resisting homeschooling, and it got worse and worse. (She holds grudges, so a number of things were wrong that I didn't even know about. Homeschooling was just one.
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Finally it came out that she felt my choices for my child were a reaction against her choices, and that I was "so different" from her, which she took as a criticism.
I thought a moment and then asked her if her choices for me when I was a child were about her mom. She was aghast, and replied that of course they were not!
"Then why would mine be all about you? We're making the best choices we can for our child, just as you did for yours."
I was afraid I had overstepped, but she got it. It made sense to her. She got a lot more supportive, even started treating me with a measure of respect. I actually ask her for advice about education now because I know she'll think it through and not just knee-jerk reject anything that isn't what she did. She and my dad even homeschooled for a day so I could visit my younger son's preschool one day. Supportive!
I don't know if that's relevant to your particular case, but dealing with the specific fears and issues that your mom has might help.
If it's just "homeschooling is bad" and not so personal for her as it was for my mom, then maybe asking her what she's worried about and then providing her with counterevidence could help.
The other thing that helped me in general with anyone who disapproved of homeschooling was my realizing that it doesn't matter what "they" think. (Whoever "they" are.) Letting go of the need to persuade people is the best thing you can do. If they judge you badly, so what? It's not open for debate. You're the mom. The decision is made. They are free to have their opinions, but it doesn't have to affect you one iota.
And if you stop feeling defensive, a funny thing happens: they stop sensing that they've found a weak point and the assaults stop. It's really kind of uncanny. So even if you don't feel 100% sure of your decision yet, no one else needs to know that unless you trust them. "They" may mean well, but if they're not helping you or your child, you don't have to open the matter for discussion. It's okay to say "We're satisfied that we're making the right choice, thanks. Now let's talk about that goal your son made last night/your lovely rose bushes/your new haircut/etc."
If you talk about their life and interests, they can't talk about your kids.
Best wishes. It does get easier.
