It's the same word. The same thing happens in Spanish padre - father, padres - parents, fathers.
I'm hesitant to ask it be marked correct, so allow me to ask (being very new at this) would this be your (singular only) fathers, or your (singular and plural) fathers? While the former is technically correct, the latter is more common, I'd think.
It can be both formal your (singular) or plural your (plural doesn't distinguish between singular/plural).
Just to clarify, does the "ь" in "батьки" create the "ch" sound that I am hearing? I thought the "ь" was used to soften the previous character?