Thank you for your email and lovely comments about my site.
I understand how shocked you are feeling. It is very normal for young children to be curious about their bodies and those of others and want to find out more by exploring.
It is best to deal with their questions and behaviour in a matter of fact way, giving them answers and information so they understand what is appropriate behaviour. Tell him that it is acceptable for him to touch himself privately in his bedroom, but that we don't do it in public, and that we do not touch other people's private parts. No one is allowed to touch his private parts not even mom or dad. It may be a good idea to find a book suitable for his age, such as 'Some parts are not for sharing' by Julie.K Federico which you can read to him. Again, when reading the book do it in a matter of fact way. At this age only give him the information he asks for.
If you see him touching his brother in the bath gently distract him by offering him a toy to play with, or buy some bath crayons to keep him busy.
Try not to react by "yelling and yanking him out the bath" as this may cause him to feel shame. In the next couple of years he will become more self conscious and will begin to seek more privacy. Children whose parents empower them with information about their bodies are less likely to seek the information elsewhere.
Good luck and let me know how you all are doing.
A note to parents: Children sometimes touch their private parts to soothe themselves if they are anxious or if they are bored. Gently distract them if they are doing it in the family room without shaming them and find ways to reduce their anxiety or boredom.
If your child displays other sexual behaviour or uses sexual words, has nightmares or sleep problems, and you notice personality changes you need to explore the situation further by consulting with a professional child psychologist.