teaghlach is a (uncommon, at least in Connemara) word for "family". Most people would say muintir for a broad sense and clann for immediate. You'll also hear gaolta. It's lenited because of the mo before it.
a chéile has a meaning of "together." With le it's just le chéile, lit. with together/ with each other. You can see it was/is lena chéile in parts still with Tá siad ag siúil lena/le chéile (They are walking together; i.e. they are courting).