whatsarobot You are a very good father and your kids will grow up having excellent taste, regardless of what they end up getting into.
Here’s a very biased list of stuff that isn’t really the same as either of the two Cowboy Bebop songs you shared, but maybe has some of the elements your kids liked about them:
Eccentric Person Come Back to Me by Masae Ohno (and really the whole album it’s from, Masae a la Mode):
Kyoko Koizumi’s album Beat Pop
Dontaku by Sadistic Mika Band
I Will Call You by Melon (former Plastics members reformed in New York, working with such pioneers as Bernie Worrell from Funkadelic)
Tighten Up by YMO, which maybe isn’t child-appropriate since it’s referencing Western stereotypes of Japanese people that your kids probably aren’t familiar with, but it is still such a great sounding song:
Oh and I’m going to recommend what @bwood just recommended to me the other day, because it is great and also immediately reminded me of Cowboy Bebop, though less so the specific two songs your kids like: