Smart or not to drive vehicle crosscountry anywhere from 2000 to 5000 miles give or take in total

It's an old 2002 neon; oil always gets changed as well as anything else it really needs, the motor is excellent and never yet had a transmission problem but it runs rough sometimes and sometimes fine and might that transmission go on a crosscountry journey; am I being naïve in thinking I could make it to/from say either or both, starting from central new York state and driving it to/from Rochester, MN and back and what about from central new York state to 3 cities in Arizona and back; would that 2nd trip be pushing my luck or might both be the end of the Neon; thx. For what u guys do and Happy Holidays!