It is lovely to hear that your mum is enjoying trips out, but being unwilling to go back is typical when they are not settled. It may be that it is too soon for trips out. Six weeks can seem like a long time for you, but it often takes a good couple of months for them to settle.
Something you can do to speed up this process is to step back from visiting every day. When mum moved into her care home I was advised to not visit at all for a week or two to allow her to form bonds with the carers and other relatives. If your mum is lonely in a place with people around 24/7 then it sounds like she is just living for your visits and not trying to interact with the carers and other residents.
This is a hard thing to do because it goes against all our instincts and we feel that we are abandoning them - although we are not. Something that might help both of you is something I did when OH was having lots of problems and I could not visit mum for several weeks. During this period I sent mum lots of picture postcards ( the sort we used to send friends and relatives when we were on holiday) with a simple message saying I loved her and would be back soon. The carers pinned these cards to her wardrobe and read them out to her regularly, so she knew that she had not been abandoned. When I next visited she had no idea how long it had been and thought I had been on a weeks holiday.
