M.P.
At her age, I'd expect to always be with her when she's interacting with baby brother. She still doesn't really understand how to be tender. I'd take her hand and softly touch brother repeating the phrase softly. Show her how to touch other things softly. When she starts to hug or kiss her brother be right there and remind her to be soft. If she's still too rough pull her back and repeat the word softly. This worked with my granddaughter when she was 3 and her brother was a small baby.
She's at the age that tantrums are common. she does feel jealous and even angry at times because she's no only THE baby. My granddaughter just turned 10 and tonight told me that she thought it was unfair to have a baby brother when she was little. Her brother just returned from spending a week with his dad. While he was gone she said she missed him. So tonight I asked for clarification of what she'd just said. She said she misses him when he's gone and sometimes she's still angry with him but mostly she's glad he's her little brother. This made my heart sing.
She's been very jealous of him for many years. I can see that she's maturing.
At 2 1/2 your daughter's brain and emotional development isn't such that she can understand these concepts. I suggest that you show her sympathy when she seems upset because of her brother being there. You may have to suggest that you understand how she feels about her brother because she still doesn't know how to talk about how she feels. You do the talking for her. When she's feeling OK, also talk about how it must feel to have a baby come in and take over her spot. Let her know that how she's feeling is OK.
I'd treat the tantrums in the same way we always treat tantrums. Ignore her and let her work her feelings out in this very physical way. I found that if I sat down on the floor a ways away from my granddaughter her tantrums ended more quickly and she would crawl over to me and let herself be held for awhile. I think I started the hugs by asking her, once she was calm, if she wanted a hug. We didn't usually talk about the tantrum or the reason for the tantrum. I just held her and comforted her, realizing that it's tough to be 3 and have a baby in the house.