How can I make my mum change the food she feeds her dogs?

My mum has a Dalmation and a lurcher (greyhound, saluki, whippet, bedlington terrier cross) who have always been fed cheap dog food. A few months ago the lurcher (8years) lost a lot of weight, she was taken to the vets, nothing was wrong that they could find and my mum took her back to get properly weighed and monitor her weight, she put most of it back on.
I told my mum to change the food because it was just cheap crap. I suggested skinners low grain food. She bought bakers instead...within a week meg had a greasy coat and dandruff and is still skinny.

I'm looking after both dogs for two weeks and the first day I had them I bought some good quality low grain food, and she gets green tripe mixed in as she's very picky and she loves it, normally leaves her food but she's eating it all. I've noticed a big change in her personality just in a couple of days.

How can I convince my mum to feed her dogs better? She earns a lot of money, I feed my dog on good quality food, and have just spent a lot of money on her dogs food because I REFUSE to feed them absolute rubbish. These are my childhood dogs and I want them to be around as long as possible, and healthy. Not lethargic and greasy coated and unhealthy....

Both dogs were washed, teeth brushed, nails clipped, tats brushed out and are exercised and fed well. None of this happens when they are at home my mum is too busy. They are not neglected, they have a big garden, my mum has land they can run around but I just feel they are much better taken care of with me but she won't let me keep them....any suggestions?