I believe it is quite common for six year old boys, especially, but some girls as well to wet themselves because they don't want to stop whatever they are doing to go to the toilet. Sooner or later they grow out of it, usually when they become self-conscious about wetting themselves.
Perhaps your daughter would consider working out exactly how long it takes her son to wash, dress etc and be ready to go to school. The child might as well learn now that on a school day when Mummy tells him to get ready, he has to do so NOW.
When he is at home after school playing there is no need to be so strict about doing things when he is told, but try sending him to wee before he starts a game and before sitting down to a meal. Mummies usually have a very good sense of how often their kiddies need to wee.