Had a similar situation (but worse, as Dad was bed bound) with my parents, OP, and I also lived 100s of miles away from them, working FT , useless / absent siblings etc. It was a shitshow. I'm also a social worker for my sins so know how it all works, how to access services, how to deal with families in crisis etc, not that it made it any easier. I'm sorry you and your Dad are in this situation. Even if not surprising, it's incredibly painful to come to the realisation that this is how your Mum is when your Dad's at his most vulnerable - not everyone is 'nice' or interested in looking after other people or understands reciprocity or can deal with responsibility I suppose. It's hard having the nature of your parents' relationship exposed like this too. It's shit.
Ask your Dad if you can contact his specialist nurse at the hospital (there should be one attached to his consultant's clinic) - explain your concerns about the home situation. Tell them your Mum won't give an accurate account of what she will support with and won't reliably do what she says she will. Explain you're worried about how this might impact on his post-surgical recovery and radiotherapy to them. Make sure they're aware of the layout of the house. Contact Adults' Services and ask for information and advice about the support that could be available to him locally.
When he's admitted, make a nuisance of yourself - call the ward, call the discharge co-ordinators and tell them all that stuff again. And have a contingency plan in place to drop everything and go there yourself to look after him - so maybe start looking into your childcare options now. You might also want to bear that in mind as you might not want carers in and out to your Dad with the Covid thing still going on. That's what I ended up doing for a short period and, although it was through gritted-to-stubs teeth running around like a blue-arsed fly while my perfectly capable but constitutionally unwilling mother was swanning about doing naff all, I'll never regret that I went there to help my Dad when he needed me.
Oh, and don't waste your energy getting into it with your Mum - if anything like mine, it made no difference. If anything, she downed tools further when challenged and took it out on Dad. Love to you and Dad OP xx