Ah, the classic "the child(ren) don't understand how dire the sutuation is and just do their own thing while caretaker(s) panic" trope.
If this is PJ and Gradient, why not say they are naturally stupidly op. Jack-jack levels of stupid op. They don't even try, their emotions go out of wack, they get scared or angry, and whoever might try to hurt them, is gone. Error keeps looking for them and is turning the multiverse upside down ("Help me find my kids or die" way).
But then they come back, maybe with a scratch or bruise, and they hug their dad. "It was scarry but it was so cool that we whooped their a-" "language, I don't need Fresh here right as you two get back" "butts." I also feel that Error would do the "Are you okay?!??" "Yea-" "Good. YOU DUMMY, WHY DID YOU DO THAT???"
They try to show their dad their cool new powers, but can't figure it out, they get frustrated and soon their emotions blow and Error sees. Que their now much more intense training while they are on the run. They need to be able to use their powers without them relying on their emotions, they need to not use their powers dispite of their emotions.
You could also throw in trauma, but not kidnapping. Real trauma, that happens to many people irl. That will give a much harder gut punch. They don't have a mom, Error isn't exactly the most kind or caring, they don't know how to communicate their emotions well. They keep moving, they don't have many friends and don't understand the bond people have with places. When their dad has friends over, somehow they always correct at least one thing, their father becomes someone that they see as "not a great guy". They don't get hugs often, no matter the words or acts of love and kindness, they feel a void from pure friendly touch.
With such shakey foundations for their lives, they would have anger or anxiety/depression issues. You could show both, having one be angry and passive aggressive, and the other trying to be a "good" kid, trying to be helpful and kind, but so scared of adding to the tension that is always there.
Error has big feelings sometimes, maybe often, and that can make it feel like there isn't room for the children's feelings (at least from their perspective).