Hand-waving just because it's convenient and makes writing easier doesn't mean the TL is realistic. I know authors have a tendency to project their own biases and beliefs onto their scenarios no matter how thoroughly thought-out they are or how good of a story they make, but butterfly nets without a logical series of events justifying them is flat-out forced.
The operative word here is "could". It may not technically be impossible, but if you're aiming for realism, then butterflying the Trump presidency "cuz reasons" isn't a decision rooted in evidence or reasoned deduction. It's your story and you're free to do what you want with it, but it seems to me we're not really getting anywhere here.
So, for the time being, perhaps it's best if I bow out. I'll return if I come up with something else.
The motivations of Obama here in this timeline are different from OTL and you don't have to understand this timeline.
But it is good if people understand the TL so we can discuss it.
The TL has a Nixon replace Agnew with Ford as running mate but failed to prevent an impeachment, the following admins were not butterlied but Obama's motivations to run here are different to OTL, it is more anti-war than the OTL which was due to the recession.
I will explain Reagan the Two Bushes and Clinton presidency if I expand on them.