Moving and Children will have to change schools

My fiancee and I lost our home to foreclosure, due to income loss. We lived together there for approx. 6 years, and I had lived previously alone with my children in the same school district. I had looked for over a year for something we could afford to rent in the same school district, and found nothing in our range. I moved temporarily with my parents and my kids, and my Fiancee stayed with friends and family until we found an affordable place. We signed a lease, but the school district is different. My children's father lives in the same school district where I am moving, about 10 minutes away. We have 50-50 custody. He is threatening to get full custody because of my change in circumstance proves instability. The place is only two bedrooms, but the landlord has agreed to let us split the larger one to have a semi- separate one for my daughter when she comes in from college. My boys are 14 and 12. He claims this is illegal and is using that against me as well. Is switching schools considered instability? Even if they live with their father they will have to switch schools, and we will be in the same district now. What are his chances of changing the 50-50 arrangement due to my moving?

You don't likely have much to worry about. You can't do much about the ex saying stupid things. You are doing what you must to make ends meet- to me it is a sign if responsibility rather than instability.
Dad would need a lot more if he wanted to get custody away from you.

He is peeing in the wind. That does not constitute a change of circumstances for custody purposes.