Is she only seeking you though because he hasn't really ever bothered to do his part
I'm wondering if you could get in touch with the health visitors and ask to referred for the sleep nurse, this is what I had to do same boat as you my little ones turning 2 this month, dad involved but not enough you aren't alone just exhausted lovely
Could you maybe try that when he gets home from work you go and get a couple hours of kip and they get a bit of time just the two of them and see if she will want him to do things a bit more?