2001 Dodge Ram 1500 transmission problems

Is a 2001 dodge ram 1500 susposed to come out of park without touching the brake pedal? The truck came out of gear from park to reverse and caused $2500 worth of damage. The engine was running in this case. However, my 3 year old granddaughter was able to take the truck from park to reverse while standing on the seat. The truck was parked at that time on a inclining driveway so it rolled only to the street.

Pulling into driveway, the truck shut off. It started back, but seemed to hesitate when trying to accelerate. The following day, the truck continued to hesitate. I added transmission fluid and took a "test drive" in the driveway to see if it continued to hesitate. It did not, but I noticed fluid leaking out of the bottom of the truck (the transmission fluid I had just put in). I had to call a roll-back to tow it to a mechanic. He said it took him a day and a half just to remove the transmission.