“they go to funerals of literally anyone they vaguely know in DH’s family. In mine, we don’t, it has to be close.” MIL is not OP’s Mum’s family, let alone close.
“I just don’t want the bloody woman at my mother’s funeral, nor did mum,” There you go, Mum didn’t want MIL there.
“Mum asked me not to tell any of her ex work colleagues until after the funeral. She wants her own children, siblings, nieces and nephews, grandchildren and a select group of dearly loved friends. That’s it.” Definitely no MIL.
“[MIL’s] non relationship with my mum. They have never shared a phone call, been to each others homes, had a coffee, not even a Christmas card, nothing. There is no relationship,” They’re not family so OP isn’t excluding family.
“My children are [MIL’s] family, (even though she doesn’t know when their birthdays are) but I’m not, nor was mum.” There you have it.
Absolutely no reason this should cause a row with OP’s husband, as this is OP’s family’s funeral – their culture, their choice. Not everyone is Catholic, shocker.
For future reference, you can choose to see all of OP’s posts and find information for yourself, it’s easy!