Getting inside doorbell to work

I recently installed a Ring 2 video doorbell. It works perfectly except I cannot get the inside doorbell to work correctly. The inside doorbell is just a dign-dong analog, as far as I know. Two wire. 20vac transformer. Simple momentary button to ring the doorbell.When I connect as instructed (no diode, wires to the ring device) there is constant continuity to the inside doorbell creating a hum. The inside doorbell is energized constantly causing a single ding then constant hum, but never a dong. Tried reversing the wire with no change. Remove a wire and the hum stops. Touch them together and apart and the doorbell rings normal. But with both wires connected to the Ring I get the ding and then constant hum.So, my questions are, does anyone know the fix for this, and in lieu of that can I simply run both wires from the transformer directly to the Ring so that it charges, and then just abandon the inside doorbell?ThanksMark