What is the normal relationship between the children's mother and the family? is she normally fully accepted, well integrated, thought well of, 'approved of'?
The reason i am asking is that, as I pointed out above, asking her not to bring the children when she has no childcare for them is basically telling her that SHE is not welcome at the funeral.
If she has a generally great and secure relationship with the wider family, then though her exclusion from the funeral may be somewhat hurtful, it need not store up further difficulties. However, if she already feels insecure / disliked / ostracised within the family, then the exclusion is going to be a much bigger issue for her (I know that all the focus in this thread has been about excluding the children - but since they need someone to look after them, you are also de facto telling the adult carer that she cannot attend either).
i was thinking about the parallel with my own family-in-law, with whom I have a difficult relationship (DH was called home and told to break off our engagement, FIL has never really spoken to 15 year old DS, his grandson, because DS looks like me etc). However, I had a very good, close relationship with DH's lovely grandmother - a down-to-earth Yorkshirewoman with a kind word for everyone.
It would be entirely possible, and within character, that DH's uncles might have sent a text or e-mail or letter, or message via FIL, to tell me that my children - and therefore I - could not attend DH's grandmother's funeral. However 'innocently meant', and however much 'oh you can come to the wake afterwards' was mentioned, I would have found that very, very difficult - a) because despite the difficulties I have with the intervening generation, I was very close to her but principally b) because it would be yet another symbol of the whole family's rejection and dislike of me and by extension my children. It would have made me very angry, and i might well have said, in the heat of the moment, that I was disgusted by the family's behaviour and the fact that they were preventing me from saying goodbye to pretty much the only member of the family I had a strong connection with.
I am not saying that this is what has happened within the OP's family - but there could be a variety of reasons, not all 'visible on the surface', why the children's mother has reacted strongly to her own and her children's exclusion from the funeral.