I’m so sorry about everything you have been dealing with, it can’t have been easy.
i have to say that I feel a certain sympathy with your siblings although I don’t think I would have gone NC in response. It feels a bit like you are laying on the ‘excuses’ as if you are trying to bomb them with reasons until they’ve to accept your decision.
This, at the same time as they and your mum are all trying to deal with and process their own grief and feelings of loss. They probably feel (not necessarily rightly) that grief should trump everything else.
It probably didn’t help if you told them about your coffin fear as they may have felt you were making everything about you, and that you were saying that their grief was not as important as yours.
I think, if I were in your shoes, I might write to each of them. I’d start by saying you totally understand their reactions and that you are really sorry for upsetting them; that the truth is you were in a very bad place mentally and were not in a fit physical or mental state to attend the funeral, although you really wanted to go.
Don’t mention childcare or not feeling you could leave your DC - I’d say this feels more like an excuse than a valid reason - but do say you were worried that you falling apart at the funeral would have been the last thing anyone would have wanted to deal with.
I’d say how very sad you are that you couldn’t be there, but I wouldn’t make any reference to the things you did before your dad died - to be honest, this isn’t really relevant, from what you say your siblings’ anger is focused on your non attendance at the funeral.
Tell them you love them and never meant to hurt them, and that you hope that you can all restore your relationships whenever they’re ready to do so.
At least that way you’ve done your best and left the doors open for reconciliation.