Normal, and actually desirable.
Please have confidence in YOUR parenting and your instincts here. Do not let your mother's very misplaced and old-fashioned concerns make you worry. Your daughter is normal -- even better, she's creative, and this will pay off later if you encourage it and don't try to squash it. Be confident in your instinct that tells you to play along with her; do not listen when your mother -- who is placing her own adult concepts onto a young child's play -- thinks this somehow indicates some mental issue of being "out of touch with reality."
At age four, your daughter has no idea of what "reality" means. She does, however, understand "fun" and "stories" and that is what the pretending is about. Unless Simone has suffered some real and serious trauma that would make her retreat into fantasy unhealthily-- this is fine. It is also pretty normal for a kid to do this for what seems like every single moment to an adult. This is a stage that will pass and is important to her development and her understanding of who she is, what interests her, and how stories work. It is NOT some sign she is mentally ill.
If she were a teen who crept home, closeted herself in her room and insisted she was someone else, and had no friends, or whatever -- yeah, reason for concern. If she were pretending violent things, that would be cause for worry, or if she were acting out inappropriate things that are too "old" for her age.
But she isn't! You describe a sunny, happy preschool-age child who is reaching out and involving you in her play. That is all good, mom. And it's normal for kids to adapt the characters they know from movies and books. So read her even more books every chance you get! I would reduce screen time in favor of books and more books, ones you read to her as well as ones she can "read" herself.
The fact she pretends and wants to involve you too means that she is very comfortable with you, mom. You want that, believe me.
Get some good books on child development that talk about imagination in preschool-age children, and copy the relevant passages for your mom. She really needs to get a grip or she's going to make you nervous (she already has) and is going to squash your daughter's beautiful imagination!
All too soon this will taper off and end and you don't want to regret that you spent these days (and months) telling Simone, "No, don't pretend."
You might even have your pediatrician tell your mom that this is developmentally normal. In fact, your daughter might end up being the kid in school who likes to write stories, or who is the one the other kids love to play with because she's so much fun, or she might be the one who is especially creative in years to come when she does projects.
One thing -- I would really consider preschool for her so that she is ready for the kindergarten classroom setting. A good quality preschool will help her learn to listen to and follow adults who are not you or dad or grandma, and will help her learn to move from activity to activity without being upset or insisting she keep doing what she's doing. If, now, she ever finds it hard to stop pretend play to take a bath or eat or do something she has to do at that time -- preschool can help kids learn that when it's time to stop doing X and move as a group to doing Y, they can cope. You can also help by telling her gently, "Simone, it's time for X. Can George go home now while you do X and he can come back later?" If she resists, see if George or Elsa or whoever she is would like to come along for X. Seriously. It won't hurt a thing.
But whatever you do, please don't listen to your mom on this. If she is not receptive to hearing this from the doctor or she rejects what development books say, you need to learn to just smile and say, "Mom, I've got this covered and Simone is fine, and creative. Please do not tell her to stop pretending. I will handle it if it's time for her to move on to another activity."
If your mom babysits Simone a lot, frankly, I'd watch for whether your mom has other ideas that show she doesn't "get" young children's development . That would be an issue, to me.