Hi L. :)
The one thing that is so important for all kids and in all situations is consistancy, consistancy consistancy. Biting is no diffrent.
The first flaw some people make IMHO is to threaten.
The second major flaw is to not follow thouugh.
(example) if you do that again I'm going to _________.
and even worse is saying that then not following through.
I know she is only a baby, but babies can and do learn from repeatedly getting the same response for both good and bad behavior.
What I was taught as a child and what I in turn did with my babies was, If they did something wrong, like biting someone, I would deal with it in that very moment.
(example) your baby is at a play group, she reaches over and bites someone. You walk immediatly over to her and pick her up and remove her telling her biting is not allowed and put her in time out, only then can you take time to explain exactly why this or that is wrong. The shock effect is powerful. And this if you do that one more time thing.. it just teaches them that they can get away with something, anything once, just not a second time.
Secondly you are the mommy! you tell your daycare how you want your child handled sweety, dont let them tell you, you know your baby better than anyone, and it a tap on the hand or leg works best so be it, if its time out so be it. Just always always give her the same response for a negative thing as well as giving her swift praise for good things.
She will learn fast what mommy and daddy expect. You dont have to be mean just dilligent and firm. Being a mom is hard work as you already know, but after a while the patterns will be set, the expectations understood, and soon enough you will not have to work so hard at it, just tell her what you expect, she will know instictively after that if she disobeys there WILL be a consequence, and noone wants that :)
My daughter went through a hitting thing for about a week, it took exactly 2 times that she hit someone she was playing with, and I walked straight over to her, picked her up, told her friend we had to go because kylie hit and its not allowed, I walked her to the car and put her in and told her, "we have to go home, no more fun today you hit someone" and close the door. or at home she hit her brother with a toy a few days later. I went straight to her, took the toy out of her hand and placed it up high on a shelf and put her in the corner (time out) and told her you are punished for hitting it is not allowed. You get the idea :)
It works for everything! and good luck!
D.