OP- IMO a father, who has a one bedroom apartment and relegates 90% of the parenting ( outside of deployment or similar circumstances) to the mother is not a great father. I can certainly understand that finances may prohibit him from doing more, but that doesn’t sound like the case. Hard to tell with what is written.
I will be completely honest. I would do what is best for DC. If I felt at the school was best for them and ex would blow that up, I may tell them to lie.