I was sure that I had seen a question like this before somewhere but I can’t find it anymore, so here goes.
Mit ihren Freunden is a Dativergänzung. However, both of your versions are correct. And forget about enforcing TKML.
Why? Because German is extremely free and flexible in its word order. The only fixed bits in sentences are the Verbklammer — that is, the finite verb being in second position in main clauses and any remaining parts of the verb (non-finite) at the end. So you get:
Position 1 - will (finite verb) - everything else - machen (infinite part of the verb)
Position 1 is traditionally filled with the fragment you want to emphasise most — often this is the subject, Julia in this case. But it could also be einen Ausflug, an den Bodensee or mit ihren Freunden. In fact, it could even be einen Ausflug an den Bodensee. Or einen Ausflug mit ihren Freunden an den Bodensee, because they somehow belong together.
Everything that is not in position 1 needs to be moved between the two halfs of the Verbklammer. The order of these fragments is, once again, not fixed. There might be some orders used more frequently than others, but only very few if any that would be considered wrong.
Since you have four different fragments, you can get 24 different possible sentences. Forgive me for not listing them all here.