she is at the age...
i think both are needed., i would start with a firm NO, this is wrong. take her up in your arms and away from where it happened , then give love . my daughter talked really well at 22 mths. we said " use your words to say how you feel, hitting hurts and is wrong, i understand you may be mad, sad, etc..please use your words, hands are not for hitting, (teeth not for biting...).
i wouldn't do a time out, just a remove from scene-with you talking and listening. i only use time outs when all else fails. and these things take time, can't expect instant results, you have to be a broken record sometimes
she is at the age and it is a change, most kids don't take well to change--
patience and good luck!

i love the book "unconditional parenting" by alfie kohn ... and it may work for you.

books.google.com/books

www.alfiekohn.org/up/index.html

From a woman who has dealt with the coming and going of lots of room mates and things, I understand how she may be feeling. If she's never had anyone move into the house with you before, it's going to be an adjustment. To her, this is her space that she shares with Mommy and whoever else typically lives in your household, I don't know your particular family situation. When you add someone else to that situation that doesn't go home after a short visit, it kind of throws off their routine. At two, I've noticed most kids like a sense of familiarity and stability in the world around them. I don't know if it's a security thing or what, but I've noticed it with a lot of kids at that age. Give her time. I know it's hard to give her time when all of the sudden she's acting like a monster, but that's what she needs. It's going to take her time to get used to having someone new in the house. Keep on reminding her that those actions aren't nice and that it makes your sister sad when she's mean like that. Remove her from the situation when she's biting, slapping, and pinching. Tell her how it makes everyone feel, and direct her towards something more positive. If she still does it after a couple months of your sister moving in, I'd start to look into other solutions because maybe there's something more there than not having adjusted to having someone new in the house.

She is testing her boundaries and also she is probably somewhat confused about your relationship with your sister as well as her relationship with her. Are you very big sister like to your sister or is it more of a peer relationship? If it is very big sister like then from your daughter's point of view that is almost like another sibling vying for your attention rather than another adult showering attention on her. This is an adjustment much like getting a new sibling. She also needs to hear from your sister. It is all fine and well for you to use words to explain to her how to be gentle and kind but your sister also needs to (in kind words) assert herself and say "I don't like it when you hurt my body, please use your words and tell me what you want." She needs to understand that she and your sister will have communication without your facilitations. I would encourage the two of them to spend time together and help your sister use the right kind of open language with her so that they establish a respectful relationship on their own. Having you facilitate too often can leave her with the impression that when you are not there she no longer has to behave a certain way. Ultimately you want her to behave kindly towards your sister because she feels she can share her thoughts and ideas with her and express her feelings and not because she is trying to avoid being reprimanded.