I live in the Clinton/Lebanon area, and my husband commutes to Newark (AND he works for NJ Transit, so I have all the inside scoop!), so you came to the right place for answers.
First off, yes, public transportation from this area IS convenient. You can take the bus from Clinton (it goes right into NYC) which is Trans-Bridge. Or you can take NJ Transit from a few different stations, and anything west of Raritan Boro has free parking.
If you decide to drive to either E. Rutherford or NYC, you would take route 78. From Clinton to E. Rutherford: 78 west to either the Turnpike or the Parkway. From Clinton to NYC: 78 right in to Holland Tunnel. But honestly, the easiest way to get to NYC from this area is take the bus or train.
Good idea to car pool with your husband. If you go that route, you would take 78 to the Turnpike (or Parkway...there are a few options). He would drop you off at Secaucus and you could take NJ Transit to Penn Station NYC. Depending on what time you leave, 78 can have traffic (if there is an accident, it's tough). But generally 78 moves. It's not as bad as you think. I'd give yourself about an hour to get to Secaucus, then an additional 20 minutes to get into NYC. If you get on the road before 7:30 (and there are no accidents), you're going to be in good shape. You can do the whole 78 corridor from about exit 15 all the way out to the parkway in about 45 minutes.
So you have a few options!
Not only does my husband do that commute, but I've also had many relocation clients move out here and do that same commute. It's very common to live out here and work in NYC.
Anyway, I'll be happy to give you more details...drop me a line and we can chat.