If the button and the mech are wired in parallel, it should work fine.
I would check all the wiring thoroughly and make sure you haven't got a grounding problem.
Is it possible that you have inadvertently wired to the NC connection on the coin mech?
I'd have to look at mine to verify, but I seem to remember that my coin mech switches have the NO and NC terminals the opposite way round to a regular microswitch.
This could possibly cause the symptoms you describe - the switch is normally closed, but dropping in a coin would open it briefly and then close it again, adding a credit.
The button would do nothing, because it is normally open.
When you remove the mech from the circuit, the button would then function normally.