Do you mean the wall & ceiling texture?

Are you sure that it is 'plaster' and not drywall compound/ mud?

Power pole sander if it is drywall mud.

No idea how you would remove real deal plaster.

Looks almost like wallpaper in the pictures.

You don't remove decorative plaster. If you don't like the finish, have it skimcoated.

I am worried that if we skim coat it, it will be flish with the trim.

A skim coat is just enough material to barely cover the top of the highest points of the existing texture. Plus, the skim coat is flush or almost flush at the molding and may be thicker at other points to cover as needed. My house had the original sand texture plaster on the main floor which neither of us particularly like. The material is cheap but the work requires either talented labor or lots of hours and lots of sanding. We compromised by having the living room and dining room skim coated and the foyer, hallway and bedrooms have the original texture. Wide open spaces go fairly quick but working around moldings slows progress.