Honestly, this would upset me too and I am also the type of person who has a hard time thinking of the "right thing to say" when put on the spot.
I would encourage you to find another care environment. If this caregiver is talking to YOU like this, imagine how she is talking to your child when you are not there...
I have worked with children for years - kindergarten teacher and day care experience and I can not imagine laying into a parent like this caregiver sounds - and I have had children hit me, and REALLY be sassy. I have been told I have the patience of a saint, but I know that is not a quality every early childhood professional possesses (unfortunately!!).
There is ABSOLUTELY NOTHING wrong with greeting your child with a smile, hug, pickup, etc. That is NOT coddling. Once you have greeted your child, if you hear she has had a rough day, then I would use a firmer voice with the child, but like you said, you can't do anything about it after the fact. That was always my motto with my students if they had a bad day - I reassured parents that it was taken care of and consequences were given during class, etc.
I would be blunt with the lady and if she says something about coddling again, I would simply state, "Excuse me - I just got done working a long hard day. I would like to greet my child with a hug and a kiss because I have really missed her today. I am going to love my child even on her sassy days. Clearly you have had a long, trying day as well, but I would appreciate not being attacked with statements regarding how "bad" her day was the instant I walk in the door!"
Don't be afraid to stand up for your child AND YOURSELF! If this care situation is not working - GET OUT OF THERE!!! :-) Good luck!!
PS...just because she is the provider, doesn't mean she necessarily knows more about how to handle kids...what are her credentials? Experience is good, but good providers also are educated...and child care is a TOUGH job with a LOT of burned out caregivers...and a burned out caregiver is NOT what is best for children. :-)