Tdy en-route or tdy and return?

This was the school you reenlisted for, correct? The school will be TDY enroute, unless it's a PCS length school. If it's a PCS length school, your orders will have the school as your duty station. If it's TDY enroute, your orders will be for your next duty station with the school dates written within the orders. If it's multiphase training, your orders will be for your phase 2 location.
As a rile of thumb, almost always TDY enroute. It's only TDY and return if your unit pays for the school.
However, at your levy brief you can designate that you want to return to clear afterwards. That is TDY enroute with authorized return to clear.

What does your orders state? If they do not clearly state that, perhaps jump to your S1 and get clarification

There is a very solid chance that it will be a TDY and return. I am doing the same for a six-month school that I'm going to. It should have been a PCS but the Army is not letting anybody PCS right now. The only way people are getting TDY in route is if the Army knows their next duty station before they even start the TDY. You're probably going to have to go down there to your school and come back to clear your base and then PCS.