LONG POST AHEAD:
I like Doctor Mora as a character; he seemed to poke at a side of Odo we don't see with anybody else. I think, like it or not, in a way he IS Odo's father in the sense that he was part of his early life. It's just Odo didn't have a very happy childhood, and it took umpteen years for them to reconcile it.
When I watch The Alternate, I see Doctor Mora realizing Odo has "grown up" and has a life. He expresses surprise at this. In this episode, he starts out seeing Odo a bit like the specimen he was, but as the show goes on his view transforms to something much more paternal. I think the creature Odo mutated into when he bashed into the containment field towards the end of the ep was, on a small level, a manifestation of how he felt in the lab. And Doctor Mora saw it.
"I've done it to you again, haven't I, Odo? I made you a prisoner. Dear God, what have I done?"
I think my favorite scene in The Alternate is Doctor Mora cradling Odo in his arms after he un-mutates. And then, at the very end, where Odo covers Doctor Mora's hand with his. Like he's seeking his 'father's' affection.
Then we get to The Begotten, where we learn a lot more about Odo's early life in the lab and we stand witness to two stubborn people seeing the other through each other's eyes. (I hope that made sense!) But they have to butt heads so hard they see stars first! Doctor Mora thinks Odo is an ungrateful brat for not "appreciating" what he did for him, and Odo thinks Doctor Mora is a gigantic jerk for thinking he should be grateful for the misery he endured before he left the lab.
I think the key turning point in this episode happens right after that adorable moment where the baby Changeling tries to imitate Odo. They walk back into Odo's office and really open up to each other. This scene never fails to make me clutch at my heart for them. Doctor Mora admits he was wrong, that Odo's constant talking to the baby Changeling helped it reach out on its own and he expresses regret that he wasn't able to connect to Odo that way--and then he ruminates that maybe Odo wouldn't be such a grump if he hadn't poked and prodded him so much. And we have Odo admitting he respected Doctor Mora, saying Doctor Mora didn't know what he was and for all he knew he was experimenting on a lump of organic residue--which is what Odo would still be if Doctor Mora hadn't made him want to shape shift. The smile on Doctor Mora's face when Odo says that is just...
Then it comes down to the poor baby Changeling getting sick again. After Doctor Bashir and Doctor Mora try everything, it still becomes clear the baby won't make it. Odo is obviously stricken. Doctor Mora could have handed him the beaker and walked out, but he presses a hand to Odo's shoulder as he walks by, a gesture of clear sympathy. Because he KNOWS what Odo is going through.
It takes losing the baby Changeling for Odo to see the pain he caused Doctor Mora. I think on some level he knew, but not to the full extent.
Which then leads to their conversation at the end of the episode...
Odo: I think I finally understand how much I meant to you... and what you must've gone through when I left.
Doctor Mora: You had to find your own way in the world.
Odo: I should've included you in my life.
Doctor Mora: You still can.
I think the pivotal moment is Doctor Mora pulling Odo into his arms and hugging him. It mirrors The Alternate in a sense, because Doctor Mora took Odo into his arms in that episode too, but there was no return embrace. The way Odo just relaxes, drops his head onto his shoulder and reciprocates(albeit slightly awkwardly!) speaks volumes. Odo finally has the warmth he's sought from Doctor Mora, and Doctor Mora realizes he is being forgiven. He appears on the verge of happy tears when Odo returns the embrace after so many years of animosity.
The hug is the moment they accepted each other for who they are, and it's the gap between them closing. What a great way to visually show something so symbolic, eh?