I think you need to draw a line in the sand tonight. Act as though it's over, pack up his stuff, drop it to his mothers tomorrow morning and tell her he's left you, you don't konw where he's gone to, but when he turns up you'll tell him she's got his stuff. Repeat to her, he's left you.
When he does turn up, don't let him in, he's left you. He chose to go, he doesn't get to chose when he comes back, and under what terms, only you do.
Marriage counselling, some time apart, I would insist on not letting him back in for at least 2-3 months (make him realise he can't just wander off). In that time, you might just get used to being a single mother all the time and not having this weekly stress.
If you want your relationship to last, you need to make this a big deal, letting him straight back in and being grateful when he finally turns up isn't making it a big deal.
Being depressed doesn't give a man an opt out of being a husband and a father whenever he fancies it. If he is mentally ill, he needs help, not just being allowed to act however he likes.
Decide if this is how you want to live your life. If it's not, you can't just hope he'll not do it next week, you have to force him to see it wasnt acceptable this week.