Oh, I know this one, having been both the bereaved person having lost my dad, and (previously and to my shame) the ‘How’s your mum?’ asker to others.
The thing is that in this context, ‘How’s your mum?’ doesn’t really mean ‘How’s your mum?’ It’s just people’s way of signalling to you that they know what has happened. ‘How are you?’ would obviously be better but could be misconstrued as a general enquiry, but most people will feel too awkward to say something direct like ‘Sorry for your loss’.
So ‘How’s your mum?’ actually translates as ‘I am aware that your father has died, and I want you to know that I have remembered and thus avoid any awkward moments when it’s unclear whether or not I am taking this into account when speaking to you.’
I expect you’ve noticed, it’ll be mainly people who’ve never experienced the loss of a parent themselves who are saying this to you. It’s because they have no idea how it feels or what to say and are just at a loss. We don’t teach what to say to bereaved people and it shows.
Subconsciously they are probably thinking that if you wanted to talk about your own feelings, this could give you an opening to do so. A response along the lines of ‘Mum is as well as can be expected, thanks, but it’s been really hard for all of us’ might possibly prompt (some of) them to enquire how you’re doing, if that’s what you want.
But try not to take it personally. One day they’ll be in your position and will realise how wrong it comes across, but until then you might just have to accept it as one of those weird British-isms that we all do sometimes.
I’m truly sorry for your loss, OP.