Am I being unreasonable to expect her to put in a bit of effort when asked my by daughter? I don’t expect every time but like I said she refuses 99 % of the time and find it quite upsetting.
YABVVVVU.
Playing an unstructured game with small children is hard work that allows you no mental space whatsoever. It can leave you drained.
I notice you mentioned that your dad plays board games and card games. That is to say - structured games where the adult gets to have a thought of their own in their head, and not play whatever part in a pretend game the child wants to play.
Do you have any inkling why your dad might prefer a structured game, where he teaches the rules, gets to have his own thoughts, and best of all, the game ends when someone wins?
Taking a small child shopping and dog walking is also hard work. It is hard to concentrate on your list and steer the trolley around the supermarket looking for your groceries while also watching a child and answering questions/engaging in conversation. And dog walking with a small child is also hard work. I don't know if you do it much, but you would understand the challenges if you did.
Please don't ask your mum to try other activities if she doesn't want to play. Baking/ gardening/ cleaning with a small child can be maddening. Do all of that with her yourself. Clean up after yourself.
I try and make sure I play with her most of the time.
This isn't really very good for your child at age 5.
She needs to get out and play with others or she will have trouble dealing with her peers in an unstructured way.
She also needs to learn to entertain herself. At five, you can start playing with her less and do more managing an activity by herself - imaginative play with toys, building something, painting or colouring, all without adult input.
Above all, my advice to you is to get your brother out of your flat and move back in there yourself. You need to establish clear boundaries between your parents and yourself and your DD. Your parents seem very well able to set boundaries but you are having a hard time getting the message. Your daughter is yours to entertain and take care of, not theirs.