We learned relatively early on in the series that Kate grew up comparing herself to her mother, and that she ended up taking the resulting feelings of inadequacy out on Rebecca, which led to them not being close.
Even when we see Kate as a child, most of the meaningful, parent/kid moments on the show happen between her and her dad, Jack.
So, in Season 2, if we were to see Kate and Rebecca perform a rad “karaoke duet” it would probably mean that a major cloud had lifted from their mother/daughter non-bond.