Jury trial for custody

I’m feeling sooo sooo defeated. Nothing period related but basically just need to vent somewhere. I’m in the middle of a messy custody dispute for two kids ages 5 and 4. My ex has not exercised his visitation in months. And the few times he’s been around sporadically he will only see our son not our daughter. I basically just never went by our court order and we talked whenever he wanted to see our son for years and it worked ok for us. Now my daughter is old enough to build a lot of resentment towards him and our son also mistreats her just like dad does. Obviously it hurts her deeply. Around the beginning of this year he started asking for my weekends instead of his and I disagreed. Especially since he’s never used his own weekends much to begin with and only for ONE of our kids. Then I got a random long ass message from a girl on fb who had a lot to say about my parenting (most of what he told her and not actually true) and claiming that she is the new girlfriend and he’s needing to switch weekends to accommodate to HER schedule. Obviously I’m not ok with this and thus he cut off all communication with me and said we will no longer coparent. I filed for sole managing conservatorship and mutually agreed visits about a month ago and he was finally served last week. This morning he filed an answer to my original petition and in it he requested a jury trial and paid a $4500 fee for it. I’m shocked and confused. He refuses to coparent with me himself but somehow believes a jury should determine the fate of my children. Has anyone gone through this? I don’t know how this process even works but to say I’m overwhelmed is an understatement. I feel financially bullied as I cannot afford a jury trial but I would have no choice. Any advice is appreciated.

Edit to add: yes a jury trial is possible for custody and I believe it is his right to request one. Texas is the only state that allows it.