Sister,
i wouldn't want to for the many questions you're already asking. i would wonder about those...subsequently effecting my own therapy, relationship with therapist, etc.
in therapy, i wanted/want someone just for me...that's going to hear me, help me, be concerned for me.
i would want to keep the two therapies separate and apart. that's just me though.

it may work for y'all if that's what you decide to do.
good luck!
Kd