Q: How do I know the difference between a broken engine mount and an ignition coil that is shot?

I have had three of the four ignition coils replaced. I notice engine knocking that seems to subside after the car warms up. Perhaps this might be resolved with another oil change, synthetic of course. But there is a shimmy at times. The car doesn't seem to have much pick up. How do I know what could be wrong so I don't get ripped off? Wouldn't the engine shake if it wasn't running on all four cylinders? There is no check engine light but it has stalled upon starting twice in the last few days and today felt like it was about to stall while I was stuck in traffic. I shifted into neutral and it idled fine. Once I was moving again, the car ran normal. I use only BP gas but even that could need a can of dry gas. I work with kids with autism and depend on a reliable vehicle. Please tell me what you think could be wrong so I don't get ripped off when I get the car fixed. I am sincerely hoping an oil change and a can of dry gas might be all I need. I need to be prepared for worse case. Thank

My car has 13409 miles.
My car has an automatic transmission.