The key issue here is that, regardless of income or children, you aren't working as a team.
If it was just you two and you were cooking dinner but you suddenly had to rush to the local postbox to send a birthday card to a relative, he would presumably keep an eye on the dinner.
It feels like he is getting resentful of doing things around the house when he is providing most of the money. However, that path will just lead to relationship ruin.
In a partnership, you both should be pulling your weight around the house. If he lived alone, he'd be doing it all himself. Whereas, in this home, it seems like you are doing the majority of home care and cooking yet he isn't recognising that contribution as he is only seeing 'monetary' contribution.
You both really need to sit down together and get on the same page as a team. Resentment will build from you as he isn't valuing your physical contribution and resentment will build from him as he thinks he is 'providing' enough due to having the bigger finances.
Strip it back. Discuss what that would look like if it was just the two of you. Assign roles, split the household jobs (if you're happy to continue doing most of the house work, despite also working 4 days per week, in lieu of financial contributions, that's fine but I don't think it will work long term as you will burn out.)
Then add the children back in. Be clear you don't expect him to do anything for them BUT there will be times when you need to lean on your partnership to get everything done and meet everyone's needs as you can't do it alone. If he is going to get annoyed about keeping an eye on his own dinner for a few minutes whilst you pick up your child, then he really needs to reframe his thinking. Would he have the same level of annoyance if you suddenly had to pop to the loo and he took over?
Financial contribution doesn't negate shared house responsibilities. I don't call working 4 days per week 'very part time', it's nearly full time. Therefore he should also be pulling his weight in the house.
If he isn't happy with the finances then I would suggest that (as you've said you pay for the food) he pays more towards food than he is currently doing and you pay some towards the mortgage instead so he actually starts to see you as actively contributing. In reality it's just shifting funds from what you are mostly contributing to, to somewhere where it's more 'visible' for him.
You both need to get on the same page though. I only work part time but we are a team and everything is split (even though he works and earns more) in a way that feels fair but, ultimately, we are married and we share finances. It's all 'ours'. This nit picking and being annoyed with each other will end the relationship if left to fester.