Ignoring the dad part
I think she'd known by the way La Manchaland fell that it wouldn't have ended well for Don Quixote, especially since he chose to remain and seal them all away instead of doing away with his treacherous Kindreds. She long since made her peace with the fact that this would probably be the last time she ever saw him, and was just determined to carry out his final will and make sure that Sancho would be free of La Manchaland and be able to go wherever she wanted (or was fated) to go. Even if it meant staying in place for a while.
Sancho it feels like she figured out what her general path would be, so set things up to make it easier to find her way (including I'm assuming telling Vergilius her location.)
Their ultimate clash would've been a bittersweet ending, but one I think Bari would've seen as necessary to give the both of them closure they both desperately needed.

I think one of the fun aspects of 'opposites attract' ships is that, at their cores, they quite often end up being far more similar than they expect/would like to admit!
Sancho appears to be a pessimist bordering on nihilism because of her lonely past, wherein she had literally no one until Don Quixote swooped in and made her into his Kindred. But even when she had a family, the main pleasures she sought out were rooted in their connection to her sire. And she hides her true enthusiasm about things for various reasons, among them likely insecurity about being openly happy considering said past.
And if Meursault is anything like his literary counterpart, he may have also had a mother who he held a connection to and whose death affected him greatly. He seeks out simple pleasures because those are just what makes him happy. He's clearly not emotionless, just suppresses his own thoughts and ideas a lot because, as he says, most people don't really listen to him in full because when he Does talk, he has so much to say that it puts people off.
In the end, they both appear to be people who put up different facades, one of overzealotry and one of indifference, because they believe that their true feelings wouldn't really be understood by others.

Um, let's see. Some basic ones...
- Because of the way their head is, they can't really eat. And they really don't need to since the Golden Bough in their prosthetic head takes care of their body's needs and keeps them up and going. Though they could theoretically ingest something through a tube in their esophagus, they tend to find it unpleasant and so avoid it. But they will hold food when with others and let someone else eat it just to feel included.
- Because of the above reasons they don't really need to breathe also.
- Deal with some chronic/phantom pain issues due to all the rewinds. Especially if they've had to rewind the Sinners several times in a single day.
- The flames on their head react to the proximity of hands/other objects getting close and reduce if something comes too near. So they don't accidentally burn other people or objects by standing near them. But if you held your hands a certain distance away you'd feel the heat coming off of it. But if you're fast enough you could theoretically light something off of the flames. The flames are nonreactive to combustibles/accelerants like gasoline.

I really like their whole vibe. I think initially Sancho would get supremely insecure about things because she'd see Don Quixote, the one person she'd ever consider to be trusted and loved, to be getting closer and closer to this strange, persistent woman who he keeps clashing with. Yet, she can't help but be intrigued by her as well. Bari is as patient and consistent with Sancho as she is with Quixote, and it would gradually endear her to Sancho.
And even after they were forced to flee La Manchaland, Bari never left her. She was always by her side. Even after Sancho wanted to forget it all, Bari always respected her wishes and just wanted her to be safe and happy.
It's a love bound by consistency, above anything else. The knowledge that Sancho can rely on her always, in presence or in spirit.