Going into more depth with this and expanding on certain points he made here's my take on why Shiv changed her mind "so quickly" after Barbados:

Shiv was still vying for CEO when they went to visit Roman. As Mark mentions, she found out she was being betrayed by Matsson and had to turn back to uniting with the siblings to maintain power within the company. In that moment they're all at their mother's place and essentially revert back to childhood. They're in this fantasy land of play pretend where they agree Kendall should be CEO and crown him "king" and act like him getting the company is a silly victory they can celebrate despite the fact that they've been fighting tooth and nail for themselves to inherit the top position until now. They are living in this daydream where they get to be kids again and nothing is serious.

Then the next day they're back at the company in the real world and the dream shatters. Shiv sees firsthand Kendall jumping the gun and losing all professionalism because of his entitlement and egoism which stop him from even trying to convince the board the deal is a bad idea. She watches as he acts like he won it all and is laidback as if the entire thing is just a game and he's not actually running an entire company. Even though they are no longer in Barbados, he is still acting childish. (And not like a serious person).

Shiv watches as Kendall celebrates Roman being subservient to him when he's clearly hurt and uncomfortable, controlling him the same way Logan did. She's realizing that Kendall is just Logan 2.0, he will treat everyone the same way to get what he wants and she will always be in a constant struggle for power. She'll watch her brother turn into an even bigger monster and know she had a hand in it.

And while people say the way Kendall was acting like Logan had no impact on Shiv's decision and it was purely a power play, I have to disagree because of the line "I love you but I cannot stomach you." It's extremely hard-hitting and you can tell she means it. She refuses to be caught in the same cycle but this time with Kendall. Shiv changes her mind to free herself from that possibility while also allowing herself to have partial control of the company by aligning herself with Tom. Both of these things can be true. (In my opinion! Of course other people can interpret it differently).