Which route you are planning from Ambala to Chindi, via Shimla or via Sundar nagar?
Though the roads are narrow but very minimal chances of road closure due to landslides.
The route through shimla is through Naldhera to Tattapaani onwards to Chindi. The roads from tattapaani to Chindi is narrow but very scenic. Do use horn at all the bends/curves to drive safe and warn oncoming vehicles.
Chindi-Karsog is another scenic route in open valley.
Chindi to Sundar nagar is also narrow and was not in a good condition when I traveled in year 2015. Latest updates can be shared by other members.
Answers for your query:
Dont go via Jhanjheli as that side has very very bad road.
You can take a high gc vehicle on Katch Jeepable road, but ask locals about condition first.
Not recommended with a child as last leg needs to be covered on foot at a vertical climb.
You can see this in above given threads.