I doubt your EX can stop you from using other care during your parenting time. Courts don't generally do that. You may have agreed with your ex during a temporary hearing or between attorneys but now there has been a change of circumstance and you no longer agree.
You are free to use whatever childcare you choose during your parenting time. I'd recommend getting custody done first, before financials. I would not recommend continuing to use your in-laws as childcare. It can hurt you in the divorce proceedings as well.
Start as you intend to go: separately. Maintain as few ties as possible to your ex and his family. That will serve your future best.
He will be free to choose where the kids go during his time as well. Accept that going in, it will make things go much smoother.