What part of hammerfell belongs to the Crowns and Forebears ?

This changes over time, and we're not entirely sure. Sentinel has long been known as a Forebear stronghold, even though the High King (a Crown instituion) reigned there. Taneth is another Forebear stronghold, and is where an Imperial navy was based while Hammerfell was part of the Empire (if you'll remember, the Forebears are more hospitable with outsiders and the Empire). Stros M'kai, Totambu, Elinhir, and I think Hegathe are all established Crown centers. Although I think Elinhir was a Forebear stronghold at some point. I'm really going off the top of my head, so don't quote me.

I used to be part of the old Oblivion Hammerfell modding project, so sometimes I forget what cities are actually part of what faction and which were simply speculated on. Full disclosure, but in the project the Forebear cities were: Gilane, Taneth, and Rihad. The Crown cities were Hegathe, Stros M'kai, Skaven, Elinhir, and Dragonstar. Sentinel (at the time of the Oblivion crisis, anyway) was officially a third party cooked up by the King Lhotun of Sentinel to help draw the two other parties together. This third party was called the Lhotunics, after the king. Naturally both Crowns and Forebears hated the Lhotunics, something they could for once finally agree on. Nothing to suggest that the Lhotunic faction survived its founder.

Edit: Yes, the 3rd Pocket Guide mentions Rihad as a Forebear stronghold. And although it doesn't mention it by name, it also identifies Dragonstar as a Crown stronghold. That only leaves really Gilane and Skaven as unknowns. Hegathe is described as a Crown city in the Great War and a few other sources.