After pressing the villainous father point, Tattletale brought up something worse she didn’t go into detail about, which Panacea desperately intervened to stop her from talking about.
I figured that was about Amy’s attraction to Victoria. Especially because Lisa’s taunting turned out right – the revealing of that secret (along with Amy’s accidental use of her power) did break up the family.
I suppose it is possible there’s another secret, involving something that can more undeniably be referred to as betraying her family than Amy using her power on Victoria and running away.