To people saying he shouldn't be going out at all: he's gone out approximately once per month. Note that the OP did not say he was paralytic when he came home for any of those times. Being able to go out with your mates once per month is eminently reasonable considering that from the OP's point of view 'he does more than his fair share' of the day to day.
It sounds like her partner would be happy to look after both kids if she wanted a night out for herself, but she herself says that she does not need or want one.
Thus the husband going out is a non-issue and completely irrelevant.
This reads like first time behaviour for him, with the prevarication about coming home, but on the other hand he'd had a massive row with the OP and now was being 'badgered' via text on top of that and being tracked via app. His response (to stay out later) wasn't the best response, but it's certainly understandable, considering he is also sleep deprived and working and trying to enjoy the one night out he has per month or so.
I don't think you're abusive, OP. I think that term is thrown around too much. Being abusive, like being a bully, is a pattern of behaviour rather than a single isolated incident.
However you may need to look at how you're coming across to him. It's weird that you say he got defensive when you told him how you felt - most partners would be consoling. From the rest of your post I get the impression that you may not have phrased things in a neutral way. He possibly felt got at because of the language you were using or the things you were saying.
I think you both need to sit down and come up with a plan for how you both get a little bit of "Me" time, whatever that means. Let him have one night per month to go out and do whatever he wants, without you messaging him. Let yourself have the same. Or if you're not interested in going out for a night, schedule two evenings a month where you go round to a friends house, or go to the cinema, or do a hobby. It's important that even if you feel like you can't leave your kids for a second, you do have even a couple of hours when you can drop your load and relax.
Keep talking to each other. Keep communicating. Try to remain calm and not raise your voice, just be as rational as possible. And apologise for shoving him.