Glad today went well!
3.5 year old, been there done that, well can't say it's all past tense. But I remember The Change. What happened??!
One big thing is communication. My daughter's first language was ASL (American Sign Language), and from all of my discussions with other parents of toddlers (and there have been a lot of these discussions, IRL and online), that really made a big difference in her frustration level. Kids have the manual dexterity necessary to sign long before they can actually form words.
There are a lot of ASL resources out there, if that's something you're interested in I can tell you more.
I'm sure you've heard of Dr. Sears, lots of great practical advice on his website:
www.askdrsears.com
General advice from me:
1.) You're doing the right thing by giving her choices. But I found that at some point too many choices became distressing for my daughter, and what she really wanted was for me to take control; I had to find that line, which I think varies for all kids. In the example with juice/ milk you gave, I think I'd probably just say, "Here, I'll leave the juice and the milk and you can decide which one you're having. Hey, see that red bird outside??" (That last part was just a random example of some distraction that didn't involve choice -- not going straight from the juice/ milk thing to "So what do you want for dinner?", but taking a break from the power struggle and just connecting.)
2.) Involve your daughter in the planning stage. I think it was my husband who introduced my daughter to the idea around then, it worked well. "First, we're going to put on your clothes. Then, we're going to brush your teeth. Then we're going to go to the grocery store! Yay!" Knowing what to expect seemed to help.
3.) Wear her out. DO stuff. This is about when the staying around the house and gazing into each others' eyes thing starts to wear thin. Make sure she has adventures, sees new things, meets new people, etc.
4.) However, be careful about the independence/ own space thing. One of the things she's testing is what she can get away with without rupturing your bond. If you show that the bond is easily ruptured, she will be less secure. If she is insecure, she will act up more. Just being there for her, being patient, and being quietly in control (without imposing control) is what will get you guys through this. Easier said than done, I know!!
As with any parenting advice, though, it has too fit with what feels comfortable to you. I know that people have taken much more authoritarian stands and that's worked fine. The very most important thing is consistency -- if you have been the sort of parent that can be described as too permissive, I think you probably haven't been an authoritarian kind of parent, and a change might well alarm your daughter and make the problems more marked. Creativity and patience.
Can give you more specific advice maybe with specific scenarios.
Good luck! Twos and threes are tough (coff) but also really really fun.