personally think that it is not a gift issue for you now. You should first ask your girlfriend's mother why she doesn't agree with you, prescribe the right medicine, and behave well in front of her.
When she is hospitalized this time, you can buy some fruits when you visit her, not too much, and don't buy any expensive nutritional supplements, so that people feel that you are trying to curry favor with her, and you will naturally visit her. Communicate more with the doctor and her more often, let her know that you really care about her, and in this process, she also knows who you are, then she will naturally feel at ease to hand her daughter to you.
As for giving nutritional supplements and the like, you can wait until her impression of you changes a little, and then launch a monetary offensive to prove that you are not a stingy person, and you are also sincere and kind to her, so that she will naturally look at you with new eyes. The above is my answer, I hope it helps you.