Can my kids’ mother move them out of state without my permission?

Since my divorce 4 years ago, my ex and I have had 50/50 custody of our kids. We live close to each other in Houston and the kids are doing really well. My ex is getting remarried and now wants to move with them to California where her fiancé lives. I don’t want them to move and I am completely capable of raising them. They don’t want to move either and leave their friends, school and sports. Can my ex just take full custody of them and move without my permission? I also want to know what I need to go to get full custody if she does move.