Pretty normal for such long trailer frames. What helped us a lot was to use the x-chock in-between the tires. Cut down the movement quite a bit. Still there, but reduced. I think you would really like them.
John & Jennifer and family
2018 Jayco White Hawk 31BH 34'
2004 Surveyor by Forest River 29'
1996 Coachman Catalina 25'
TV 2010 Dodge Ram 2500HD SLT 4WD SB CC
2002 Jayco 12UTD PopUp
Have the same camper. Shaking and wiggling have always been somewhat of an issue and seems most notable in the front bedroom. I've found that placing about 10" - 12" tall wooden blocks under the four corner stabilizer jacks seems to help. Seems like the less the stabilizer jacks have to extend, the less shaking there is.
2018 White Hawk 31BH
2013 Silverado 2500 HD
Wobble stoppers are in your future. Easy to make, or you can spent big bucks $$$.
Made mine for under $50.
2x4s, ratchet straps, and eye hooks. 2xs length is roughly 2 1/2 to 3', dependent on your tt.