The use here of "Ihre" confuses me. I originally thought it translated to Her pants not your pants.
As far as I know, "Ihre Hosen" can mean "Her pants", "Your pants"(because of capital 'I' - the formal "you"), "Their pants" and "It's pants"
I think the last case is 'its pants'. Apart from that you are absolutely right.
Is this pants the English meaning or pants the American meaning? (ie, knickers or trousers?)
Trousers. For underwear you could say Wäsche or Unterwäsche. There's also Unterhosen, but I don't think that word is used that often.
How are Germans not confused with sentences like this when you could be talking about multiple people's pants?