I also am keen to reply, have been waiting for the kids to sleep so I can do my best to articulate it all -but still not sure how to - will try -
Its really really hard, on both of you. I think in my experience the Dads find it harder to adjust to life with a child. When my first came my DH didnt get it at all, and thought life would be the same and was happy to go on holiday without us etc etc, things I couldnt comprehend, but by number 3 hes settled well into it and weve settled into our routine - hes hopeless overnight or in the early morning so I do that, and Im at my tiredness at bedtime so he does the fun & stories then.
I wonder if things that could help you guys could be -
making sure you have time for yourselves, set it into your routine, routine it all out on your schedule so everyone knows when that is, makes it sooo much easier for us.
making sure you have time set aside together, doing adult thing together, may be much easier for this when your DD starts school, doing a pub lunch together or something, or date night takeway when DD is in bed is possible etc, weve found a fab pub with a soft play in it that works so maybe something like that - bringing child fun and adult fun together?
This is also important to remember - as DD gets older the things they can do together they both enjoy will increase - my DH loves gaming with DS and reading Harry potter with DD, our youngest DD is too little for that stuff yet but easier for us as weve seen how things will go in the future - find a common ground that they will both love - football? gaming? swimming? running? what does he like? what did he like before kids? theres often a feeling of loss of identity that all parents get (not just adopting) and finding a way back to yourself that includes the new reality of kids is soooo helpful, even eating fish and chips on the beach, anything that spans both generations of what we find fun?
I think having a routine really helps, espcially if you are doing so much of the parenting and the housework, putting it out in a schedule to give all the needs met time really helps as then everyone knows when their needs are met and when they are expected to do fun/the jobs etc. If you can afford it get a cleaner or whatever you need to cut down the non essential stuff to focus on the family, if it feels a crisis time cut back on all non essentials like cleaning & go back to coccooning time?
You will get more time when DD is in school, and as they get older their interests are more fun. Star wars comes about age 5/6 for example, i know that was a great fun time for my DH, the kids start getting interested in cool stuff and you can guide them together?
But also DH does need to work with you on the parenting, there will be some differences on style (im the nagger but gentle, DH is fun but strict when hes strict for example, the kids see that) but basic stuff needs to be on the same page. I wonder if spending time with other families may help? I dont know, but I do know what chatting about this stuff while relaxed and at the pub while kids play in soft play is a more productive way of doing it than by having it out with him while tensions are high.
So, id say, start slow, a plan in your head and a routine on paper, make some changes, make some time for yourselves,dont even have to make it a thing, just say ooo i really want to watch this ... and the cinema, or ooo .... said theyd babysit so we can go out, or .... find this pub with a soft play lets try it, etc etc, anything, even movie time after bed time chaos, and reconnect and slowly slowly things may improve.
I guess im saying, this will get better, its hard now but can improve, baby steps to improve things, time will make more of a link between kids and adult fun.
Who knows, maybe hel be great at the teenage years? I do think some Dads find the little kids so boring. maybe have him watch Bluey on cebebbies(accidently of course while you all relax one time??) for some great Dad stuff.
I think too if you suspect hes depressed but not keen for GP help, get him out excercising? would that help? family swimming is such a good bonder, a place with water slides, you maybe are 'too scared' to go on and and needs a daddy daughter splash? or get him into running with DD, she may love it?or whatever his sport may be?
Most importantly your doing fab. 4s are really hard.