In my opinion, and experience, it’s not effective to insist that a spouse do something she doesn’t want to do. For example, if my wife is staying up too late and I say, “Go to bed,” she will not listen; instead, she will just get angry.
For this reason, I suggest you encourage him to go to a minyan not by lecturing or bugging him about it, and not even by mentioning it at all, but instead by being a good example and getting into bed early enough so that (if he follows your example and goes to bed soon after) he will get enough sleep to be able to make minyan. Nowadays it is way too easy to stay up too late, with artificial lighting and the internet and smart phones and such. We all need to devote considerable willpower to going to bed at an appropriate time.
An ironic thing about this thread is that I’ve seen stories of well-known rabbis advising their students to daven b’yechidus if necessary for shalom bayis reasons. I personally know people who, more frequently than not, have to daven alone for shalom bayis reasons (to help with the kids, for example).
In any case, while davening with a minyan is very important, it is not required if one has a really good reason not too — and being so sleep deprived you’re in a horrible mood and can’t function (if that’s the case) seems like a good reason. So as long as it only happens sometimes I wouldn’t see it as a horrible thing.