Lack of core activation and full-body tightness, particularly during upper body pressing exercises, is a common training mistake.
Because a majority of these movements are performed while either lying or sitting on a bench, it's easy to become neuromuscularly complacent while allowing much of your body to relax. Not only does this reduce the amount of force you can generate, but it can compromise form, posture, and lifting mechanics.
Perform single-arm variations of your favorite dumbbell pressing exercise, like the dumbbell bench press. You should be capable of using the same load for the unilateral movement as you would during the bilateral counterpart (both arms working in unison). So, if you can bench press two 100 pound dumbbells, you should be able to one-arm press a single 100 pound dumbbell.
If you feel like you're about to flip off the bench using a 70-pound dumbbell but you typically handle 100-pounds in each hand, then you're probably lacking significant levels of core activation, rotary stability, and full-body tightness.