Kids are much tougher than we give them credit for, and they don't carry the tension around in the muscles like adults, which actually means they are far less likely to get hurt on a ride such as BTMRR than we would be.
That being said... at 42 inches and 4 years old, if your child would like to ride BTMRR I think he/she should be given the opportunity. I was never one to hold my child back from doing anything she wanted to try, unless their was a height requirement set by the park for safetly reasons. She was riding the log flume at Busch Gardens at Williamsburg when she was 2 1/2 years old. My husband would have had a stroke if he had been with us (he is the overprotective one), but she wanted to go, there was no height restriction and she LOVED it. In fact, so much so, we had to put off her first trip to WDW because she didn't hit the magic 40 inches until she was 6 and all she had talked about was riding Splash Mountain, so we knew there would be a problem if she could ride the flume at BG, but not at WDW.
Anyway, let him/her give it a try. If you don't want to take her on it, let another member of your party. In fact, that may be even better, because if he/she senses any fear in you, it may rub off on her.