I have a friend with 2 DC ages 4 and 2 now.
Ist DC he had a full on nervous breakdown...work stress? Got better, very hands on dad from age 1, super at doing nights etc. Put it all in the past.
DC2 same thing. Left work, stopped caring for himself, totally useless to support wife. Around 9-10 months on...got new job, started doing stuff again, now super hands on involved and functioning husband and father.
He now does all cooking and shopping, works, takes DCs to childcare, does night wakings etc.
They will not be having any more DC...because he for some reason can't cope and his wife was near to breaking point last time (even though they have a large and supportive and local family)
I don''t know the answer to your ? because I don't know whether, like my friend your DH is super the rest of the time or if he's just slightly less selfish which you accept and work round.
My ExH on the other hand was selfish to the core and just got progressively worse as time went on with each child....which sounds more like yours if he's so disengaged from family life.
Tell me that it is better when he goes away...go on...I bet it is!