Jamie's loyalties

Jaime's loyalties have not changed. He left so he could keep his word, which is a thing that has become important to him. He did not break up with Cersei and will not turn his back on the Lannister cause. He only intends to do something he deems right and who knows which form this will take? His intent is to find a way to re-conciliate both Cersei's rule and the war effort he thinks is owed.

He is a fool, this I must say at this point. Cersei is right and the two idiots (Jon and Daenerys) are not to be trusted with anything. They'll just make a bloody mess of whatever they touch and Daenerys remains a declared enemy. You don't help the person you know will come for you afterwards.

Cersei thinks everyone is a fool until proven otherwise. She's right again.

I didn't see it so I cannot have a very detailed opinion. What I gathered from what I read was that Jaime objected to breaking his word. His decision was not motivated by the way Cersei treated him. Did she lie to him or did she only inform him after the deal was done? The latter is not the same and while Jaime has a legitimate desire to be consulted about such decisions, he is not in charge.
Was he upset about being left out of the decision making process or did he simply disagree with the decision itself?

Seeing the dragons changes nothing. Only fools need to see things happen before they realise they really are as people say.
Cersei knows how dangerous Daenerys is. She is actually more dangerous than whatever lies beyond the Wall. This is why she takes the risk of not helping her. Let her go ahead and get killed first. Could the Night King be a threat at all if he hadn't been given a dragon to bring the Wall down? Most probably not.

This whole story is playing with people's willingness to follow irrational, feeling- or fear-based assumptions. They believe in the danger of White Walkers without question, just like they are willing to believe global warming is man made the moment someone tells them so. I have no hard conviction on the global warming matter, I believe we do not really know and I see how a part of the political spectrum bases careers on people's fear of it. It doesn't mean the threat is invented, by the way, only that it is being misused, the same way priests of antiquity would extort sacrifices from those who believed in the influence of gods.

Now we'll see Westeros divided in a good side of dumb believers who swallow whatever they are told and all join forces together to go get slaughtered and a side of evil sceptics who ask questions and won't jump into the fire at the first command of the "well-meaning party".