Wait… I don’t remember them forcing her to drink with her. They only walked up to her and asked her to have a drink with them. Though they were a little rude by asking her, but they only approached her and didn’t block or force her.
While still a strech I think the forced part is because of face. It would be rude to deny your guests a drink as the host-family. She couldn’t have said ‘no’ without it becoming an issue between countries (remember, all three are princes) and it would reflect badly on her grandfather and the in-laws. Sure, she could’ve something less extreme than beating them up but this way she can guarantee this is the last she hears of it.
They won’t go around telling their friends and family that they were beaten up but an upstart princess refusing to even drink with her important guests would’ve been gossiping material for years.