Hi Hduenejsi so,
1st guitar I had was a dreadnought (it's a bit beat up now but I still use it) and, initially, had a similar problem. There are a few things that might help - using a strap, and/or standing, using a foot rest - (along with a million gimmicks for sale which are probably rubbish). Back in the day I just percevered, now I'm comfortable with any guitar on my lap or standing (never tried one of those big Jazz things though). It may seem like a large obstacle now but if you stick with it, the movement will go away and you will become comfortable with the guitar. Think back to your 1st times on a bike/skateboard/driving a car or similar, and the discomfort involved at the time.
If you're worried about it you could try a one-on-one lesson with one of the tutors. Someone at your local guitar/instrument store will probably be more than happy to help too.
Hope this helps.