What powers the contactor? (The big one, not the relay.) If it's also powered from the 50VA xmer, quite likely when the relay contacts close, it causes a large voltage drop, resulting in undervoltage to the relay coil, which opens the relay contacts, and with the load now off, the voltage builds back up, closing the relay contacts, dropping the voltage..... All this happens very quickly, hence the buzzing of the relay.
The reason you see an arc across the contactor control contacts is due to the larger current needed by it's bigger coil. Any AC coil draws a large inrush, then much less when it's sealed in. When you hold the pushbutton down, eventually the big contactor seals in, thereby reducing it's current to a level the 50VA xmer can handle.
A general purpose xmer can't come up with much surge current, a control xmer can. The control xmer has more iron in it's core, thus it's heavier.
If this is the case, you'll need to grossly oversize a general purpose xmer, or get a control xmer that can handle the big contactor.