Practically speaking, you could arrange with your sister for your DM to split her time between UK, Switzerland and Mexico. When in Mexico you or your sister visits her. 2 months here, a month in Mexico, 2 months Switzerland, one in Mexico, 2 in UK... etc. You pay for her to fly first or business class when she’s more infirm, which would still be cheaper than legal fees, care costs, medical costs, etc. She doesn’t get lonely, you’re not scared that every time she leaves it’ll be the “final goodbye”.
One day, you will say goodbye to your DM for the last time. It happens to everyone (death). Being in the same house or the same continent does not protect you from that.
I’m sorry your mother is lonely. I get that it’s hard, I really honestly do. Particularly this year, it’s make anyone feel a long long way from family. But. A lot of elderly people in the UK are also lonely/can’t move nearer family due to disparity in property prices, or there family are overseas, etc etc. This is a situation people face. I know I sound cruel, but ageing and death are cruel.