Is the GOP party breaking apart?

[DC Al Fine]

In short, no. There is no practical alternative. Parties SHOULD have big tents with diverse views.

This. The American electoral system tends towards two parties. Breaking off and forming a third party provides no rewards, unlike in a PR or Westminster system. If you need to be part of a party covering ~50% of the population to hold power, you will have to accept some diversity in your tent.