Is your 2yr old ready to TT? My boys didn't TT till just after 3.
Its hard & frustrating at times when you feel like they should be ready but its easier (trust me) to wait till they are ready.
I think if he is showing signs/potential that he is ready to TT then 3 nights a f/n shouldn't impact the process too much. Summer is coming so use that to your advantage with lots of nappy free time.
I wouldn't push the issues with your ex, just do what you can at home & pack a potty/toilet seat for him to take on nights at Dad's when you feel he is ready to do it there too.