Suzuki Cultus might hit from bottom at few rough patches and at some speed breakers on road from Muzaffarabad to Dowarian as it will be fully loaded, but road's not that bad and is manageable. Although it's a bit narrower than other roads in northern areas we are used to.
I would recommend you to stay at Keran instead of Dowarian as better accommodation options are available there. You can easily get Jeep from there, go to Ratti Gali base camp, trek (on foot or horse back) and come back within the same day. People do stay at camp site near the lake, but I personally wouldn't choose that place for staying with my own family. Not because it's unsafe, but because using common makeshift washrooms would be a hassle for families.
Taobat is a very beautiful and a must visit place in my opinion. There are plenty of hotels where you can stay with family. Although you'll need jeep to get there. Road after Kel isn't suitable for cars. You can use your own car up to Sharda or even Kel, but not after that.