You are allowed to drive the entire length of the Garden State Parkway to the NY border with your MH. Trucks are not allowed north of exit 105. As you should recall from your post last week, there are some arched bridges over the parkway between about exits 135 and 150 stay away from the far right and far left lanes in that area. The heaviest traffic on the Parkway in also in that stretch of road. Avoid the rush hours.
When you get to NY you can either go east over the Tappan Zee to I684 to join I84 at Danbury or go west up the NY Turnpike to I84 and over the Newburgh/Beacon Bridge. I84 takes you to the Mass Turnpike, which you likely already know.
We're headed down to Assateague late next week. We hate reservations as we are never sure of our exact departure date. How crowded was it while you were there?
Also, we live a few miles east of Parkway exit 105. Give us a wave when you go by.
alid posted above while I was typing. He is correct that the lanes are narrow in the northern section of the Parkway. If you want to avoid that section, you can get off the parkway at exit 127 for route 440 west, which changes it's name to I287 after a few miles. Exit 127 is on the north side of the Bridge over the Raritan River. The northbound Parkway splits just before the southern end of the bridge and you want to be on the right side of the split. It has been a while since I used that exit and I think there are three lanes on that side going over the bridge. I think you need to be in the center lane for the 440 westbound part of the exit. Watch the signs carefully. This is a situation where GPS lane guidance would be helpful.
We have run into traffic on the I287 route as well as the parkway, but at least there are no tolls and the lanes are wider. If you go that way, the Newburgh/Beacon bridge is the better way as well.