Assuming that your 2001 Neon is similar to the 1995 Neon we had, replacing the motor mounts should be something you can do at home. If memory serves me correctly there are three of them – two of which are very accessible. Not sure about the third. I replaced the front motor mount in our '95 with no great problem using just basic tools. A typical arrangement in passenger sedans is three mounts – one on each side of the Engine and one in front.
Why not send your husband out to take a look at the job? The only specialized tools required are wheel ramps (or jack stands but they aren’t as safe) if the front mount has to be accessed from under the car. He should NEVER even think about working under a car supported only by a jack.
And he’ll need a decent floor jack to support the engine while he is removing and replacing each mount. You replace them one at a time of course. And be careful not to accidentally punch a hole in the radiator if the front mount has to be accessed from above.