I would have been fine with it, except shoving him up the stairs and then shoving/throwing him across the room onto the floor was a bit much...especially since Frodo is so much smaller than Aragorn.I can see a good reason for Aragorn to do this, as distasteful as it seems. After seeing the little "show" put on in the common room, Aragorn probably had a vision of the entire enterprise failing right on the spot.
He had to impress on Frodo that not only was Frodo's life at stake, but the fate of all the free peoples, too. With stakes that high, a good, healthy shove would not be out of place as a way of emphasizing the point. It certainly got Frodo's attention.
Great interpretation! Also, what if Aragorn was trying to make it clear to the unsavory types at the Pony that the Hobbits were his business? If you're a part-time Doer of Evil, are you going to want to mess with a Ranger who's obviously concerned with this mess? Aragorn got Frodo out of the common room without fuss, and into his protection. Who cares if Frodo's feelings are a little hurt, it'll prepare him for his long journey.