Hi. Try consulting a lawyer. Recently, I had some legal issues and I found on Yelp about the lawyer Bechara Tarabay. You also need to get in touch with a lawyer soon.

Technically, he has a right to challenge you for custody and for child support. A judge will likely have to make a ruling. But odds are very good in your favor because courts are heavily gender biased in favor of women and almost always give women primary custody and the chunk of his paycheck that comes with that. Homeschooling, as long as you are square with the state agency that monitors that, won't be an issue. Slightly more than 80% of the time, women win primary custody. As a woman, you generally have to be in jail, a non-recovered druggie, or a convicted child abuser in order to not win primary custody from a man. Enjoy your court-room advantage if you want to use that type of leverage against your children's father.

Now, if you were TRULY interested in the children's best interest, you'd figure out how to share parenting time 50:50 and accept that neither of you should lay claim to any of the other's paycheck. If that happened, the children would be much happier and healthier. You might not like hearing that, but all the reputable, unbiased child psychologists will tell you that.