it is 100% ok to go on ur own car. cars can go upto Kel easily. but after sharda road conditions are not good so u can hire a jeep from Keran for the round trip or just to drop u if u have plan to stay in Kel.
As far as hotels are concern. Sangham is very old hotel now. Rooms are smelly my choice for the muzaffarabad is Mir Continental. the setup is new and rates are reasonable. Food quality is good. In Neelum Valley AJK Resorts are the best option with good facilities at best locations and reasonable charges. U have to get advance booking for all the AJK resorts. As i just visit on start of May this year. Let me knw if u want any other help