So what kind of things are going on the credit card - your personal spends (clothes, haircuts, work lunches, daily coffee) or household/ child costs (food shopping, child’s clothes/ shoes / classes or activities)?
I’d say that household/ child costs should come from joint money, not your own money, but that might be harder to split out with the way you and your DH/ DP seem to organise your finances - I’m guessing he pays most bills from his account and you pay childcare & food from your account. You should not be expected to contribute equally to finances due to the disparity in your income - something like a 75:25 split would be fair.
In my experience, it’s a lot easier with a joint account as well as your own personal accounts. We have a joint account for everything household/ child/ food/ pet related costs, and know how much needs to be put in there each month to cover usual monthly costs plus any extra costs like birthdays, Xmas etc.
The monthly amount is split between us (currently 60:40 as I work part-time). The rest of my money is mine to spend as I want. This makes it easier for me to budget as I know how much free money I have each month.
As to the feeling of imbalance in your relationship, I think that happens a lot when one partner (and it’s usually the mum) goes part time or becomes a SAHM. You do sound as though you’ve let things drift a bit by letting DH deal with all the finances - this is disempowering you as you’re not aware of the full financial position. Does he acknowledge that you going part time means you do more childcare/ household stuff? Is there a reason he can’t do any of the nursery runs (commute etc) or has it just fallen to you bu default? Have you thought about how to manage when your DC is at school and you need to cover holidays etc? All things to think about if you’re feeling uncomfortable with the way things are happening now.