Families are shaped by the worlds that they live in; nothing happens in a vaccum.
The Price family as we know it today began when Thomas Price, late of the Covenant of St. George, married Alice Healy, last survivor of the branch of the Healy family which began with Alexander and Enid Healy's departure from the Covenant. There's a reason the modern Covenant considers them "a lineage of traitors."
Alice and Thomas were happy. Not happy ever after, but happy long enough to have two children, even if Thomas never saw his daughter born. Their son, Kevin, went on to meet and marry a girl named Evelyn, who had been raised by unlikely adoptive parents: a cuckoo and a Revenant. Every family has its secrets, I suppose. Their daughter, Jane, tried three times to quit the family business, before marrying a nice man named Theodore Harrington. Pity he turned out to be an incubus...
Kevin and Evelyn had three children: Alexander, who specializes in reptile and psuedomammalian cryptids; Verity, who specializes in sapient city-dwelling cryptids; and Antimony, who specializes in explosives, pit traps, and driving everyone around her to distraction. The family has never been larger, and one focused air strike could still take them all out.
It's dangerous to be a Price...and there's a Price for everything.