Everything could be put down to both of you being really tired except the name calling. Of course people get stressed if they've worked all day and need to keep going with cooking, cleaning, parenting but usually this can be vented in a way that isn't cruel. He could say to you "look I'm so tired, can we sit together and work this all out, something needs to give" or "I get that you're ill so have a lie down but do you think you could help out later by sorting the washing or bathing the kids and I'll do the rest". That's being a team.
I wouldn't be able to get past the name calling though. If you work part time, I assume that you aren't in a situation where you work all day and get things like lunch breaks and tea breaks? So your day is pretty much drop offs or hand overs, working, parenting, cleaning etc. It's not like you get that half an hour or an hour everyday where you can switch off and just eat your lunch like he gets to. I know it seems such a small thing but getting a lunch break at work with no children around and switching off from work really is something that keeps a lot of working parents sane.
I'm a part time worker like you OP and I really do parent then switch right to work mode after I drop my DS to nursery and I don't get a break at work because I only work 5 hours a day. So I literally open my eyes in the morning and it's go, go, go and the only time I really have a moment to myself is once my DS goes to bed but even then I have a zillion things to do because I have an SN child so I'm doing the more than words course so I need to do my reading and form filling for that, work out his appointments, plan childcare almost a year in advance etc. It feels like my mind doesn't stop.
I think you need to sit with your DH and firstly tell him that name calling is not acceptable and you won't tolerate it. If he thinks you're being lazy (you aren't) he can talk to you like an adult about it. Also explain to him the load you have on your shoulders. He probably isn't aware of just how much you do and have to think about because he's out at work all day. What's wrong with a bit of mess that you can both spend 20 minutes cleaning up once the kids are bedded? Why does it have to be immaculate while they are awake because if you clean it up, like you do, they'll just make a mess again. Make him aware of this. Tell him he needs to be able to cope with a bit of mess when he comes home as it's normal and can be done later on. If he responds well to all of this and apologises for what he has said to you, it's worth a go and staying together but you need to be on the same page and have the same priorities.
I would see your GP as well because it sounds like you are really stressed and stress will make everything you catch 10 times worse. It seems like your DH is exploding and getting it all out but you're sat there keeping it all in and slowly killing yourself inside. Please making him aware of this as soon as possible