Essentially the core relationship dynamic are this. In the original source material, Bo had trouble finding any kind of stable relationship, and Merlin and Morgana's potential feelings for each other were pushed aside because of their inability to properly talk about their feelings until her time with Morgause turned Morgana against Merlin and their other old friends. This time around, the addition of Bo to life in Camelot allows all three to find what they were looking for, as Bo's defiance of the usual rules inspires Merlin and Morgana to accept their own feelings for each other while also falling for Bo at the same time.
Lost in Camelot
When Bo, Kenzi and Merlin learn that Bo is a native of Camelot's time and was sent into the future by the Norn, Kilgharrah explains that this means she cannot be sent "back" to the future without creating a dangerous rift in the world. The "Heartwarming" part comes in when Bo asks and Kilgharrah confirms that it might be possible to send Kenzi back to the future, but despite Kenzi having just been complaining about factors such as the toilet facilities and the lack of good music, she immediately rejects the idea of being separated from Bo, preferring to stay in the past with her best friend rather than return to the future.
Bo, Merlin and Morgana's reunion in Chapter 35; after Bo was captured buying time for Morgana to get away, Morgana is finally able to acknowledge that she loves Bo, persuading Bo to accompany her to a private location so that she can tell Bo how she feels directly. When Merlin comes to join them, as Bo watches Merlin and Morgana kiss while she's wrapped in their arms, the succubus who spent so long without a family reflects that she feels like she's home.
In Chapter 42, Merlin finally tells Arthur the truth about his magic and his relationship with Bo (Bo has already told Arthur what she is), and Arthur agrees to trust Merlin and work on helping protect other magic-users once he becomes king, even comparing their relationship to his own feelings for Gwen.
While Arthur and Gwen were wrong to assume that Bo was cheating on Merlin and Morgana, once the situation is explained to all parties Bo is quick to assure them all that she doesn't blame anyone so long as they all accept the situation. As the triad reveal the full details of their magical heritage to Arthur and Gwen, while both are shocked to learn that the three are all creatures of magic the future king and queen each accept that Bo, Merlin and Morgana being good people proves that magic is not evil in itself despite Uther's beliefs.
When Bo and Morgana learn that Merlin is anxious around Mordred because of the prophecy that he will kill Arthur, although Morgana just wants to ignore the prophecy, Bo finds a compromise that both of them can agree with, getting Mordred aware from his current guardian of Alvarr and taking him to a more peaceful group of druids who will help him avoid his more violent destiny.
While it's mixed in with Tear Jerker as Morgana volunteers to sacrifice herself to stop the sleeping curse, it ultimately reflects the positive impact their relationship has had on the trio; where Morgana focused on her own desires in canon, here she chooses to sacrifice herself to save the kingdom and the ones she loves from the consequences of her own mistake.
The Lost Kingdom
Despite the loss of his wife and daughter, as well as a considerable culture gap, Trick/the Blood King does his best to recognise Bo's reasons for being reluctant to take an official role as his heir, even as he and Bo work to establish their dynamic as grandfather and granddaughter.
Once the curse has been broken and Bo reunites with Merlin and Morgana, Bo immediately assure Morgana that she doesn't blame the younger woman for being tricked by Morgause. Bo's own experience makes it easy for her to understand why Morgana wanted to believe that her newly-discovered family just wanted to help her; as far as Bo is concerned, Morgause tricking Morgana like that says more about Morgause as a threat than Morgana. This leads to the three sharing a session of Glad-to-Be-Alive Sex, with Bo's thoughts making it clear that she particularly enjoys the new large bed provided to her.
Even without Merlin to serve as an active Morality Pet, Arthur shows true compassion for his friends when he claims responsibility for Kenzi and Gwaine stealing food and drink that was set aside for Camelot's upcoming guests at the melee, even though he only just met Gwaine and Kenzi isn't a close friend to Arthur himself.
Merlin and Morgana might be regarded as lower-class servants in the kingdom of the Fae, but when they attend the celebration to announce the return of the lost princess to the fae kingdom, Morgana reflects that she's happier being able to publicly attend such an event with Merlin than she ever was when sitting at Uther's right hand in Camelot during similar parties, even if she's relegated to the back with other servants.
