Wow - you are going through a lot! Barely recovered from pregnancy and birth and now returing to work, and maybe sleep deprived too. That is enough to put alot of stress on you.
Know that your baby loves you. Some babies prefer mom over others for a while. Recall how for nine months she could hear your voice and your body provided the best environment for her - now she is out in the cold, cruel world and has found a safe place in your arms. Thank goodness that she is able to comforted by someone (YOU!) as there are those babies that are not able to be comforted by anyone. Sounds like she is also a baby who needs more touch contact than your son did. Over time, she will be able to separate better - 6 weeks is very young; and yet you have the additional pressure of returning to work at this time and how will she react to a caregiver situation - doesn't make you feel very good, but she is not trying to irritate you. Remember that your baby is not out to get you or make you feel bad - she is who she is! She may very well be picking up on the stress you are feeling of her needing to be held and also her being unwilling to let others comfort her and the fact that she is a different temperment than her brother - she is a sensitive little girl who is aware of subtle changes, like the different between grandma and mom or dad and mom. Over time, she may come to prefer one of them too. But for now, you are her world.
I always tell moms not to expect too much too fast. Some babies are more attached to their moms and that is a good thing that she has formed this bond with you - though it makes returning to work harder. I hope that you have a caregiver who will have alot of patience to work with her and be calm as she transitions to this new schedule and care person - it will take time. Just as it will take you time to adjust.
She may also be more willing to accept an alternate caregiver when you are not present.
I am sure she will grow up to be a sweet, sensitive person who was glad her mom was there to pick her up when she cried and comfort her. Dad will get his turn too - just not yet.
My three kids, all preferred being held to being in any mechanical device and that meant that the house cleaning and my own needs had to go on the back burner when they were babies. But now that they are grown adults, I would not trade all the hours of rocking, walking and singing lullabies that we spent. It is so worth your investment as a parent.