The second sentence:

They visited Brighton, which they went to Northern Ireland after

makes no sense to me. I would expect:

They visited Brighton and went to Northern Ireland afterwards.

To go to a place means to visit a place. You can substitute go to for the verb visit.

Did you visit Northern Ireland?

Did you go to Northern Ireland?

They visited Northern Ireland, which they went to, after seeing Brighton.

They went to Northern Ireland, which they visited after seeing Brighton.

They went to Brighton, after which they visited Northern Ireland.

They went to Brighton and went on to Northern Ireland after(wards).