It is strongly recommended that you take all the necessary medication for yourself and your kids, like paracetamol, ibuprofen etc because you don't know how far a hospital or doctor would be when needed and it is better to be prepared.
Make sure you have enough fluid and things to eat with you in the car, as the journey from Manali to Leh is not like other routes where you would find lots of places to eat. There are some long distances when there are no places to eat or drink. So it is better to be well equipped especially when going on a long journey with kids.