Bronze Buckshot's family was actually pretty wealthy, but then she met Arko while she was on vacation and was like "oooh exotic beefy yak man hot <3" and oops! baby time. Her parents kicked her out when they learned about the impending yak-pony bastard child and Bronze started living in a lower district of Canterlot. When her kid was born she took her to Arko in Yakyakistan and begged him to raise her there until she could at least afford to send her to school, and he agreed. Young Suki lived happily in the mountains with her big yak papa, but when she was eight, Bronze came back to retrieve her. She was very obviously embarrassed, ashamed, and guilty about having Suki in the first place, and she mainly just took her back so that she would stop feeling bad about it. Arko didn't particularly want to give up his kid, but Bronze was her mother after all, she had final say. In Canterlot, Suki learned to be quiet, polite, and basically just stay down and pretend she didn't exist. Her mother did care about her, but she also cared what other ponies thought. She taught her daughter to behave so they wouldn't think she was raising a wild, unruly yak 'brid. She certainly didn't want ponies to be afraid of Suki. Unfortunately, that kinda shit breeds major emotional problems later on in life. Rotgut resents her mother and sorely misses her father.
Gear Grind and Palm Frond met when Gear was between cities and Palm was out on a scouting mission. They talked, hit it off, had a short fling, and Palm ended up with a clutch. Three of the halfogriffs were healthy little feathery babies, but the fourth was born without wings. A kid like that would be a detriment to their siblings, their mother, and themself, so Palm Frond dropped them in the nearest pony city and took the others back to Mount Eris. Gear doesn't know he has kids, and Palm is fine keeping it that way. She raised her remaining kids with help from friends and family, and while she wishes she had been able to keep that last hatchling, she's confident they're in good hooves.