Do dependent sources work in two directions?
No, VCVS as well as other voltage/current controlled sources are only one-way.

You're just creating a short-circuit between two voltage sources. One (The controlled one) want to set Vin*K, the other (v2) wants to set 1V.

An ideal transformer model (not to be confused with the ferromagnetic transformer model, which includes ALSO but not only an ideal transformer model) is maybe what you're looking for.