Hi Sally. You haven't said what your Mum's feeding system is. We used to have a tall round stob with a cross piece at the top and feeders hanging from that. The rats loved it

They shimmied up the pole with no problems, but it made them stand out well for taking aim with an air rifle. We covered a couple of feet of the pole with manky grease, which deterred them a bit, as rats are surprisingly fastidious and don't like getting their feet greasy. Now we have a metal pole, purpose bought from Dobbies, with curly sticky out bits at the top and both peanut and seed feeders hanging from those arms. The seed feeder is the type with a large saucer stuck to the bottom so in theory the birds don't scatter the seed over the edge. That bit doesn't work so we do get seed on the ground, but most of it is eaten by ground feeders such as yellow hammers, howling doos (collared doves, beautiful but they do screech), hungry blackbirds, pheasants etc. I suspect the mice also crawl out of the foundations of the house to munch at night, but we've seen no sign of rats. Your Mum already has the rats though so they would still visit but as long as the pole is well away from walls, overhanging trees and so on, they shouldn't be able to get up there. The same might apply to squirrels.
Peanuts must always be fed from a mesh feeder, as birds have been known the choke on whole nuts spread on the ground or on a flat birdtable. You can get feeders for peanuts which keep the squirrels out, supposedly - worth a try? Or just give up and enjoy feeding whatever arrives?
How to stop the birds scattering the seed over the edge of the saucer I really don't know. Ungrateful little $@@$
All I can think of for that is to have concrete under the feeder so your Mum can sweep up at dusk.