Can anybody recommend a hotel in Trogir with parking.
You should know that the historic center of Trogir is accessible for pedestrians only -- no vehicles. There is a parking lot just to the north (across the canal) that is an easy walk, and there is also short-term parking on the island very close to the center where you can park just while checking in and bringing your luggage. You might want to check out the Hotel Pašike. I don't have personal experience staying there (I stayed at an apartment and can't recommend any hotel from first-hand experience), but it might be the nicest and closest to the parking area.
Your only alternative for a hotel with onsite parking is to stay somewhere away from the center.