I live 45 mins drive from Bhimber. There is nothing extraordinary in that city.
IMHO, here is what should you do;
Leave for Mirpur (AJK) early in the morning, you'll reach Mirpur in 3.5-4 hrs depending on your driving style. There you have plenty of choices for night stay i.e medium class hotel like Roopyal hotel, a bit upper class like jabeer hotel and high class like Regency hotel.
Enjoy the beautiful view of Mangla Dam and give your child a boat ride in Army Water Sports Club Mangla.
After that you can visit upper jehlum canal which is situated on 15 min drive from Mirpur. You can also visit the the tomb of the great sufi poet 'Mian Muhammad Baksh' which is in kharri shareef, 10 min drive from Mirpur.
Then you can visit jaatlan head. You can go inside mangla dam where old hindu temple is located (depending if water level is low enough, it is reachable nowadays and un-reachable in monsoon season).
You can go to hot water spring 'tatta paani' which is located on 2:30 hr drive from Mirpur.
You can visit kotli in 2 hrs. Also peer gali, jandi chontraan, nakyal and kaladab if you like hilly areas.
If you have any questions regarding Mirpur and surroundings, feel free to ask.
Wishing you happy journey.