Student and teacher bathing together:
It is forbidden for a student to bathe together with his Rebbe. If however he arrived to the bathhouse before his Rebbe then he is not required to leave. Likewise, if his Rebbe needs the students help in the bathhouse, he is not required to leave. Likewise, the above prohibition only applies in an area that it is accustomed to bathe unclothed. If however they wear bathing suits, then it is permitted to bathe together.
From the letter of the law it is forbidden to bathe together with your father, father in-law, step-father, brother in-law and some add even with your brother. Practically, the widespread custom today is to be lenient in all the above.
May a father bathe with his young son?
It is questionable whether the above prohibition applies towards a young son. [Practically, the custom is to be lenient, as stated above.]