I'm sorry, I didn't see your response to me.... how about you wait 3 more months, doing what you are doing, and see how things go with her? that will give her 3 more months to be really comfortable with preschool and having so many more children in her classroom, and time to get comfortable with having a baby brother (although this is always in flux, since now he can't take/touch her stuff, but once he starts to crawl he will be able to.... so that relationship will always be evolving)
Perhaps you can try to give her short responses to her... Mom, Mom, I don't want her to play with me. What if she takes my shovel" stuff - sometimes (and I don't know you are doing this, obviously!) as parents/teachers we ignore a child because a) we're TIRED of behavior but also b) because we think if we don't give attention to it then the behavior might stop. And that's true, to a certain extent, but in this case I think you need to stop, handle the issue, then say "and now we won't talk about it anymore." So, Mom, Mom, Mom, what if she takes my shovel? you say "Oh, then you will ask for it back, and if she doesn't give it back, I will help you."
But Mom, Mom, what if she pushes my sand castle? "Then you will tell her to stop and I will help you. BUT she looks like a nice girl, I think she'll play nicely with the sand."
But Mom, Mom... 'DD name, that's enough. We're not talking about this anymore. You are fine. Let's have fun in the sand."
And help her get involved in building with her shovel, bucket, whatever. And if she "mom, moms you, tell her 'enough, it's time to play." Mom, I love you. I love you, too, DD, now let's go get some food at the table. Let's go find a place to sit to have our snack."
PERHAPS this will help her, because she seems to be going over the same ground over and over, working herself up. You need to give her the tools to help herself, remind her you wlil help, too, and then stop the perseverating.
I think it's time for some playdates at your house with ONE friend at a time from school who is a nice, easy going, not pushy and bossy kid. (this might be a boy, girls sometimes are the bossiest things at this age!) I know it's not your first idea of fun, given you also have a baby, but I think it's time for her to practice having friends. You can plan for 1-2 hours at the MOST - probably 11/2 hours is best - and plan to do something specific. Invite the child over to paint a picture, or to play with playdough. Or to play in the water table/in the wading pool (although that might be hard because they have to share stuff). Can you stand to make cookies together (think those easy pillsbury dough logs of cookies: kids each slice their log with a plastic knife, put on baking pan, bake, and voila, they think they baked cookies!) Think of something where each child would be at their own space at the table, with their own equipment, so they don't need to share their stuff. (put them at each end of the table, for example, so that poor child doesn't take your daughter's brush and she go ballistic!) then hover. have DH take DS out, anywhere, or have them at home but DS is DH's responsibility so you don't need to deal at all (DS takes a bottle, right?)
hover gently, but hover, so if something happens and the child takes your daughter's shovel (and it would be good if this happened once for practice) then you say "DD, what do you say to Mary/Mark? 'that's my shovel, I need it. Please give it back." Mark/mary, what did you hear DD?" Believe me, the child will give it back.... and play will continue. Keep the time very short so neither child gets to the end of their rope, and so it's mostly a positive experience. Remember things will happen, perhaps not the first time, but the 5th or 6th, and that's fine because that's kind of what you want: for your DD to see that she can handle the bad stuff, and that you are there to back her up.
Find 3 kids who work well with your daughter and have the kids come over one at a time. And without their parents, because you don't want to have to focus on entertaining the adult, or dealing with the adult's issues with their kid (or worse, perhaps they LET their little darling take shovels, etc...) - you need to be hovering kind of inconspicuously (you'll dust the same area of the counter, wash the same pot over and over....) Not all parents will allow a child of 21/2 yrs old or 3 years old to do a playdate without an adult, but if you explain that your daughter is having a hard time playing with so many kids at school, that you want her to have time with just one friend, perhaps it will go over better. Or worst case, you have the other adult there, but again, get DH to take DS out so you aren't also focusing on nursing, putting baby to bed, etc. And don't let the other parent suck you into the "oh, let them work it out, they'll be fine" because that is actually CORRECT for other children, but you really probably don't want that attitude with your daughter since she's such a nervous nelly re: working it out.
Lather, rinse, repeat about 1000 more times. Ask the teacher which children your DD seems to get along best with.
Oh, now that the teachers have helped her get comfortable by shadowing an adult, what about pairing her up specifically with another child (a gentle, helpful one - every classroom has one of these) so it's "DD, mary, why don't you go build with legos/go paint a picture? Or, if Mary is painting a picture, the teacher brings DD there and says "it's time to paint a picture next to Mary." and the teacher stays RIGHT THERE but doesn't make too much commentary about 'oh, what a nice picture, isn't it fun to paint with mary?" just keeps her mouth shut so she fades into the woodwork. this might work better with dramatic play, or lego building, but you get the picture. eventually the hope is that Mary will finish the picture, and then say to DD 'let's go .... read a book, cook in the kitchen, whatever" and DD would go along. Not the first time, but the 10th or 11th time? or if Mary is playing with a ball outside, teacher does the same thing 'Mary, how about if DD joins you and you play ball chase?'
I had a boy, Nicky, who was my go-to for new kids in my preschool room - he was the bestest boy ever, and he would play with the kid and (I swear) caught on to what I was doing and then a few days later you'd see him approaching my target child to invite to play.... wonder what Nicky is doing? He's probably in his late 20s/early 30s? oh, god, I'm old... he actually (at 4 yrs old, mind you) remembered which kids had already been picked when playing duck duck duck goose and would choose one who hadn' been picked yet, even if that child wasn't one of his close friends! that's unheard of with 4 yr olds..... although something tells me KAM's son is probably like this?
Now, if things are about the same in 3 months, I'd have a heart to heart with the pediatrician when DD isn't in the room and get some help. She's very tightly wound, and it might just be a tiny bit of family coaching from a child's therapist would help you all help her to unwind and relax. She might also have some sensory stuff, or whatever, that isn't helping matters (ask her teacher; will she sit at circle with the other children? what happens if another child accidently brushes her arm when they are reaching for pens/markers/brushes? what about during circle if a child touches her accidently when they are playing pass the bean bag, or just settling in to be able to see the book better? can she stand at the sand table/water table with a group of other kids or does she have to be on her own side, not standing next to anyone?)
I'd lean more towards the tightly wound, let's see if we can figure out ways to unwind her vs. jumping on the sensory or other special need train....