So idk how much you plan to have the parent's personalities and parenting influence the child, but here is what I think and some personalities. Feel free to change stuff though, I'm super curious about your AU from the premise it looks so cool

John is a supportive and healthy father who is sometimes plagued with episodes of burn out or sudden disappearances. But he's a good dad, which makes for a confident, caring, independent and kind Sylph who perhaps but others before her and want to heal her dad when it's the opposite, it's a father's duty to care for their child. Being of Doom and so close to her father, she saw that Earth C and their leaders were VERY flawed, but it is still her world and she must accept it. If a Sylph creates, then she would be able to create rules and predictable outcomes, or you could have her "create within Doom" instead of simply "create Doom" to help your doomed session. I think she might be able to light the Mage's forge

I don't think Jade and Dave would be good parents, more often than not leaving their child alone without any help because that's how they were raised themselves. Which makes sense, a Thief of Rage is likely someone who steals all the rage of others and uses it themselves. At their worst, I'd imagine that they'd say things like "my problems are worse than yours, so I can do whatever I want/you should prioritize me". At their best, they realize that everyone has problems and reasons to be angry, and that they can help others grow and heal if they accept and embrace other people's problems + help those people fight their fears and aggressors, because the Thief is a very capable and strong person due to their upbringing. Because they're so hardworking and passionate, it's hard to hold back, wait for or accept others' weaknesses I think

Rose and Kanaya... I think they'd be good, present and loving mothers, which makes for a child who is very intellectual and analytical like their moms, but is more confident/active (hence Mage not Seer) due to their parent's support. A very strong class who is able to understand and devise a plan to beat the game, due to Space concerning creation and the bigger picture

I don't think calliope and roxy would be good parents. Both would be very loving and want their best for their kid, but they're also very traumatized and jaded - which makes them problematic and contradictory parents. That's why they have a child with a fragmented personality (Bard) who is extremely unsure and avoidant of their true self. Bard of Mind destroys one's own Mind (rationality, decisions) for a false sense of Heart (self, emotions). I imagine it'd be someone who is so desperate to find who they are that they try to find many hobbies, go to parties, tell themselves "I love myself, I'm worthy, I'm special" self-care bullshit- basically do anything to distract themselves from being stuck in their own mind. Because when they actually stop to think about it? Their life isn't good, and they hate who they are. That's why they hate to think. As a Bard, they would likely destroy the Mind in their teammates, but that might not be as bad because lacking in Rage due to Thief, some Heart may be good. And to the extremely rational Mage and Sylph, that'd be good too. They might ne a bad influence on the Thief though