In life this is how sometimes there are problems where they are less expected. The daughter is on the threshold of puberty, which in itself is a very difficult period for every teenager. Especially for parents, puberty and adolescence can be a meticulous process in which they try to maintain closeness to the child, enable it to become independent and mature, and at the same time set limits.
Her daughter lost her mother at six and she remembers very well. You also helped her and her mother, who partly offset her loss, to help her remember her. The girl idealized the image of her mother, who has not been there for a long time. In your situation this is expected. The same thing happens often with adults when they lose a loved one. After the death of his wife for five years, you have devoted most of your time and love to your daughters. At the same time, they were intensely attached to each other and especially the daughter was attached to you. With the arrival of a new partner in her life she is in a situation where she feels very much at risk. She is afraid of losing her attention and love. She experiences the partner as an intruder who wants to steal her father and force her mother's place.
It is important that you understand this in your feelings and be tolerant of it. Your daughter needs very open conversations with you as well as some time to feel that your fear is redundant. Keep an attitude unchanged about it, as you have done so far. Explain the situation to her openly once and for all. Emphasize that you still love the same and that nothing will change between you, explain the difference between love of parent and partner. The girl is old enough to be able to accept a rational explanation, she will also understand that you want to be with your partner on your own occasionally.
But it will take time to make the changes, which are big and very stressful, internalized. This will also greatly help your mother, who really likes you and expresses this, awaiting your new relationships. She should talk about it with her granddaughter, too. And you yourself need to be sure to act right. You should not even think about giving up your relationship with your partner because of your daughter. Pay attention to your possible emotional blackmail and do not pick it up. Her role as father and the role of a partner or husband are not excluded, but they are exactly in their complementary diversity. As a man who is loved and satisfied, you will be just a better father and not worse. I want you to succeed in the new relationship. This way, you will be able to give your daughter the best traveler in adulthood, an example of a successful relationship of loving partnership.