Searches of "trollopsing" brings up a result in Poems and Plays of John Masefield where he uses the word. I also found it used on a Key and Peele sketch.
Otherwise, I can't seem to find any indication that it's a real word.
Is it a word, and what does it mean?
Edit with example: "I stayed at home for the past fifteen years taking care of mom and dad while you've been trollopsing all over the world."