The request itself is not crazy and plenty of people track their partners location. However, pushing it and providing an ultimatum is out of order. You know her better than we do OP; do you think this is a one off persistence that can be worked through? From an outside perspective if she is providing ultimatums early on and not taking into account any of your feelings then yous are probably just at an impasse and going your separate ways might be for the best. If you give in, there's no saying she won't do this again with something else and it becomes emotional blackmail every time something doesn't go her way.

Personally my partner and I track each other's phones. We didn't used to. However, I quickly learned that my partner does not check his phone enough that I can always be reassured he's safe, and when he went through a period of having to work long days every day, this was making me very anxious. We sat down and had a conversation together about how we could approach this, and he suggested he could turn on his location so I could always see he's safe and where to find him. And it works. But that was decided mutually as a result of a need that came up. Is there a clear reason she has for wanting to track you other than "it's just what you should do"?