I have an explosive child, I do know how hard it is. Lots of children aren't like that at all, but quite a few are. So while it might not be the norm, it's not unusual either. Lots of children still have tantrums up to 5 or 6.
LOADS of children will behave beautifully at nursery and school then explode when they are at home so I wouldn't read too much into your mum's comment. I hate to say it but I don't you'll get much help from GP. Maybe look at council parenting courses for strong willed children instead
What I WOULD say is this:
She can want things her own way as much as she likes, but that doesn't mean you have to give it to her. You can empathise AND set boundaries. Look at Big Little Feelings and Dr Siggie on Instagram.
Your mum's reaction tells me a lot. She obviously struggles to cope with big emotions. And lo, so do you. I wonder if you were allowed to have big emotions and fully express yourself as a child? I wonder how she reacted when you demanded something?
Explore this and work out why your daughter having big emotions and setting boundaries is so hard for you.
Then work on your own self regulation so you can stay truly calm in the moment. They're just feelings, and she's allowed to express them. You can still set boundaries. You can still stay unruffled. It's not our job to keep our children calm and happy always. You're the parent and need to be calmly and lovingly in charge to make your child feel safe, and at the moment it sounds like your DD is in charge?
Once you have this down, you can then work on coaching her to express her feelings through words, recognise when she's starting to get wound up, and on what else she can do when she's starting to feel that way, practise calming things to ward off explosions.
Do you have any other concerns about her behaviour?
What are the triggers for meltdowns? Can you spot any patterns?
My child's behaviour is mostly anxiety driven. Something to consider.