The classical argument against a third party is that it weakens the movement. I.e. if the Republicans split, the result would be two parties that were weaker than the Democrats.
I think this is a myth. Notice how Lieberman ran as an independent but said he would caucus with the Democrats, hence not weakening the Democratic leadership.
I think if the Republicans split, the two halves would be larger than the original one party. If the Right to Life side didn’t get involved with a bunch of other stuff, they might attract Democrats who are Right to Life but for some other reason won’t support the Republican Party as it stands now.
In fact after celebrating and then sobering up and seeing how the two other parties were stronger, the Democrats would split too!!
But remember, parties to a great extent are state organizations. It could be for example, that Republicans in Alabama would just all move to the split off party which was more Right to Life. California, might have both of the two split parties.