Do you have a weekend schedule?

One of the things I read is that kids need a predictable pattern for stability and security. If he can't do weeknights could he do every Friday night?

Rather than asking which night, could you start changing this (sorry if you already are) to...

'I would like you to look after the kids on x night this week'

Or

'If you wish to see the kids this week then it will be x night'

Or

H has a default night and you will only do that for him if he agrees a swap to another night of your choosing.

He might still let you down but their would be no ambiguity about it.

Both mid 30s, 2 young kids
BD 7sep14
XW moved on long ago, now living with OM1
D paperwork in progress