Trump isn't "trying to exploit a rift in the Dem Party" with his Squad-based trolling.
Trump isn't trying to divide the Dems. I heard that a couple of times on CNN today. That's wrong, imo. And, no, Trump's a-hole "go back where you came from" tweets didn't somehow backfire and unite the Dems. Far from it. Trump got exactly what he wanted out of those tweets, as usual.
What Trump is trying to do is win the debate against him by picking the people from our side whom he prefers to make our arguments for us. Always argue with the people from the other side most likely to make an unpersuasive case for their own side (in terms of the target audience). In this case, Trump wants the "Squad" from our side (talented but inexperienced newcomers) to have the spotlight. Pelosi is too much for Trump, and he knows it, so he wants to relegate her to a backup role by "personalizing" (which the media eats up) an attack against the Squad.
Trump's also not "throwing red meat" to his misguided yahoo supporters, imo. They are already in his pocket. What he is actually doing is very cleverly appealing to Obama voters who went for him in 2016 and to suburban moderate Republicans who abandoned the Republicans in the 2018 mid-terms. He's doing that, not by saying what those voters want to hear, but by stage managing the Dem microphone/spotlight access and manipulating the media.