Q: Front end vibration

By rotating the tires, you may have brought tires from the back to the front which have "road force variation" which was not as apparent when the tires were in the rear. Note that even brand new tires can vibrate due to lack of quality control and tire design deficiencies. As a first diagnostic, I would put the tires back where they were and, unless a mechanic’s inspection immediately found other plausible causes, you might have to have the tires checked on a "road force" type balancer. Also, the only way to be reasonably sure that a tire/wheel assembly is actually balanced is to have the technician balance the assembly, then completely remove the assembly from the machine and re-install it in a different position. If it still reads balanced in the NEW position, then it is probably balanced. But, what you will often find is the assembly won’t read balanced and that is because of technician error in mounting the assembly and/or the machine is simply not calibrated. Always ask the technician to remove and re-install the tire/wheel assembly if you really want to get what you are paying for which is a balanced assembly.

If the vibration becomes marked on gear changes, that might implicate a rotating component in the transmission or the torque converter. There is also the possibility of a defective harmonic balancer. With regard to the engine mounts, if they are not OEM dealer supplied, that would raise some suspicions and that is why, on a part like that, it is so important to use dealer supplied parts because once you install the "knock-off" if you end up with a problem like the one you have you are then literally in a circumstance where you are diagnosing BOTH possible defects in the "knock off" design and actual problems (in this case, vibration sources) that exist elsewhere in the vehicle.

The bottom line is you should request a vehicle vibration diagnostic. It is possible to use remote chassis ears (wireless microphones with an in-cabin receiver) to narrow the origin of the vibration and, if it gets really complicated, there are frequency domain analyzers that can take the noise from the vibration and decompose it to likely mechanical sources. My guess is, if you request the diagnostic, it will probably not get that complicated because, from what you are describing the vibration is marked, and consequently to a trained mechanic the likely origins will be obvious. If you have additional concerns or a follow-up on this, don’t hesitate to re-contact YourMechanic.