I feel like, if mcu loki had kids before asgard being destroyed, actually even before finding out he is jotun bc he has always being too much othered, he wouldn't fully trust the servants/nannies/those people that take care and teaching stuff to nobles kids but i don't know the name exactly, like, I imagine him and sigyn going to their baby's nursery and taking them to their room, people would complain they cuddle them too much and loki would be like "well, at 3 am my child was crying and no one except for me and my wife came to see whe he needs".
and spending time with thor only supervisioned, (sorry for annoying you and info dumping you with my headcanon ...) bc one day when the baby already knew how to walk, the managed to escape the nursery and walk by the palace's corridors, then thor found them, and thor brought them to the trainning area on his shoulder, then loki found them both and like "it is not a place to bring babies".......
(okay i will stop ...)
I mean I always liked the headcanon of Sigyn and Loki being way more hands on with their sons than what's expected from royalty. Their own parental issues making them to want to be more close with their children.
Another headcanon being for as much happiness and love Loki's family brings him he can never take true comfort in it. He's too full of self doubt and insecurity to not believe something going to ruin this bit of happiness that's just his. Yeah, if he fond out about being Jotun after having Narvi and Vali it would completely destroy whatever balance Loki had in his family. He already believed he was just a tool in canon when found the truth and it would break him all the more to have that burden be projected on his children.
Loki would never trust Thor alone with his children. Although Thor would insist and plead he could be trusted with his nephews. Loki would require someone else be watching Thor before he's allowed to babysit