I have a well-known complete lack of tact in these sorts of matters. If I approached him, it would be something like "Dude, grow a pair, tell your wife it's game night, and if she doesn't like it, tell her she can kiss your 20-sider. If she gives you any more lip, tell her she's cut off. No more nightly deliveries from Mr. Happy."
If you provoke a confrontation of any sort, you will only lose a player.
I would take one of two approaches, depending on the rest of the group.
Approach one is to switch to a more flexible arrangement of game days. That is, you don't play every Saturday, but instead aim to play one evening every two weeks or so. The key to making this work is three things:
1) Everyone must come to the session with a reasonably accurate note of when they're free to play again. Before anyone leaves, you need to fix a date for the next game. (If a player can't make it to a session, they need to let the group know when they'll be available next, or else they'll almost certainly miss the next session... and very soon be an ex-player.)
(Also, people need to provide a diary that they can reasonably stick to. So, if your 'problem player' is having his schedule dictated by another, he needs to have the discussion with her
before coming to the session so he can set up the next game with confidence. Otherwise, this just won't work.)
2) Everyone needs to be commited to actually gaming. When scheduling gatherings (of various people for various reasons), I've seen a lot of people answering the question, "when are you free?" with one or two 'ideal' dates. Obviously, if everyone does that, then you may well find there are
no dates when everyone will play. Instead, the answer needs to include those dates that the player
could be there, even if it's not quite ideal.
3) Once a date for the game is set, it needs to be treated with the same seriousness as any other commitment. If people merely 'pencil in' the date, but overwrite it as soon as anything else comes up, you'll get lots of cancellations, and your group will disband. (Obviously, this doesn't apply to the occasional emergency - sometimes things really do come up.)
If, for whatever reason, the group can't work like this (perhaps your player's wife can't fix her schedule in advance, which means he can't, either), I would instead propose that the group have a fixed game day that suits as many people as possible, but is very flexible about attendance. Basically, everyone should aim to "be there when you can", but not stress out about it.
For this to work, I recommend that the DM keep all the character sheets, and all the PCs gain XP and treasure at the same rate, whether the player is there or not (so that people don't fall behind, and find they can't contribute to the game when they are there).
Of the two, the first approach probably works best for a small group, where there are likely to be fewer scheduling conflicts but less resiliance to absenteeism, while the latter would work best for a large group (as getting people's schedules to mesh will be difficult, but the group can survive missing a few people). The latter approach also works best if people can't be sure when they're available, or if you find you're getting a lot of people calling off.
Whatever approach you go with, it's probably a good idea to monitor how it's working out fairly constantly. It may well need tweaking as things change. If it doesn't work, change the system - don't try to force people to change to work within the system you've agreed. If all else fails, consider moving to a virtual tabletop.
Good luck!