"Why would he do that and then spend so many resources to get her back?"
(1) use her as scapegoat in the trial
(2) kill her himself so that no other liability is out there in the open to expose him
(3) check if she's pregnant and would cause a future liability
All of these are more plausible than him actually falling in love with her. That man has not been the sweetest person to her thus far. In her eyes, he is still her employer who has a tight noose over her neck.
She wouldn't have survived in Gimora for this long if she ain't smart
Interesting points, but they don't really hold up to me.
1) Idk, I'm pretty sure he doesn't actually need her specifically to be a scapegoat and that he's capable enough to figure something else out. Killing her so she can't be used against him would be easier with how unpredictable she can be.
2) I don't buy that he wouldn't have already killed her in that case.
3) Again, I'm pretty sure outright killing her upon finding her would have been easier. Unless he intended to take the child for whatever reason, in which case he still wouldn't need to act the way he does with Adele, pretending that he's scared of her leaving and showering her with words of affection.
I do agree that him being in love with her seems extremely unlikely on Adele's side, given how he's treated her. But the point was it seems to me that Adele is getting hung up on thinking he's lying about loving her rather than how he's treated her and what sort of person he is, which very much is emotions getting in the way of thinking.
Caesar has been nothing but an asshole to Adele. Sure, his actions might have given away some kind of affection for her, but can she really trust that? For all she knows, this might be another one of Caesar’s rich-guy selfish whims.
That man has everything: power, money, influence. Does it even make sense for him to now claim that he loves a mere shoe-shiner who doesn’t have anything that is considered as desirable in his world (aside of course for her face and body)? This might as well all be another of his whims to bed her and dispose of her (offers which he has made plenty of times already)
Keep in mind, Adele doesn’t know yet that Aegir moved on his own to give her those gold coins. To her, that behavior was more like the Caesar in her mind than a lovesick puppy.
Again, Adele isn’t in the wrong for doubting this guy’s motives since he has been nothing but a manipulative rich jerk since the first time they met. She couldn’t have survived Gimora all these years without being this guarded and doubtful about everything that could put her in danger. It’s up to Caesar now to change her mind. And what a mighty task that would be indeed.

I feel like she's getting hung up on the wrong thing here. Based on his actions, it's pretty evident he genuinely believes he loves her (and his emotions seeming to be closer to obsession is another thing). And it was not him throwing her out personally. Why would he do that and then spend so many resources to get her back?
However, he still hasn't shown that he isn't a dangerous person to her or that he respects her and her wishes, and THAT is pretty significant whether he loves her or not.
Sidenote, I don't think his parents truly left because they were so in love they'd think nothing of abandoning their kid.