I don't think it is necessarily all over for you if you don't want it to be, but you cannot go on as you are.
Firstly, you need to look after yourself better. Driving that distance every day is really dangerous, I commute about 1 to 1.30 hours a day and I find that plenty, much over an hour each way and you can really risk being tired and falling asleep at the wheel. Can you get another job nearer to home, go on the train or stay there a couple of nights a week? (it sounds unthinkable for a mum but plenty of men do this) Or move nearer to the job.
I would also sort out your own sleeping as you have to sleep to be safe to drive and able to do your job, so sleep on your own or if he's not in bed by X time, then say he can sleep on the sofa/airbed that night. You cannot be woken up by him every night, but I wouldn't wait for him to realise the game is ruining his marriage, I'd make sure I was getting a good night's sleep before tackling the rest.
I don't excuse what he said, but it very much seems like a lashing out thing to say (inexcusable, but have been known to say nasty thing myself), only you know if you think it had some truth to it (I very much doubt he really doens't love his child).
Get the cleaner, no question. Don't even ask him, just get one and then at least that's one less thing for you to worry about.
Once you have the driving,sleeping and cleaning a bit more under control, you can then focus on your marriage. I would just tell him straight, I can't go on like this and your game is going to break us up as I'm just not prepared to put up with your half-heartedness about us. Tell him that he has to do the housework and cooking when the children are around (not in his work hours) like everyone else.
This may not be insoluable, doing things like gaming (or going on MN) when you should be working is one of the problems of home-working (but I work late into the night to get my work done). But you are doing everything and must be physically if not mentally exhausted and you probably can't keep this up for much longer anyway.