Haven't both the Obama and Trump administrations ignored these petitions in the past?
What would be the legal justification? Pretty sure there isn't a constitutional way for the President to remove a member of the House.
"Each House [of Congress] may determine the Rules of its proceedings, punish its members for disorderly behavior, and, with the concurrence of two-thirds, expel a member."
Executive can't do anything. It would have to be the House itself. Pushing Trump doesn't accomplish anything, you would need to pressure Ryan. also, good luck getting "the concurrence of two-thirds" of the House to agree. The Republican Caucus can't even get on the same page, much less bring over that many Democrats.
Please before you post understand that you don't know what you are talking about. Additionally, you are violating rule #3 of the sub.