Hi ER,
Discipline and teaching children to understand boundaries is SO important and starting as early as possible is key, as long as your discipline is age appropriate. Times outs for 3 yr olds is appropriate, yet each child may react differently to different T.O. techniques. Also, get used to your little one "reporting" any and all home activity to daycare, especially if she thinks it'll get attention.
Here are some things I've found most helpful with my children...Time Outs DO work for them - they HATE them. I've found a couple corners and chair that are in our kitchen & family room works best (where we are 90% of the time and gives mom/dad more options). We save "T.O. in your room" for more serious issues. For my children, it doesn't matter where they go to T.O., they just HATE getting removed and losing their freedom. My children face the wall & cannot watch what's going on w/everyone else (otherwise they play) - you don't have to do that, but this is what works for my children. So, you may want to try a T.O. location near you but removed from activity. We use a consistent technique: 1) tell them firmly the specific behavior is unacceptable (and why..."it hurts people"), 2) march them to the corner/chair/etc. without saying another word, 3)set them in the corner and tell them to stay there until YOU say it's time to get out, 4) if she doesn't stay, quietly replace her until she stays, 5)after the designated time go to her and explain clearly why she was in T.O. and appropriate behavior, ask for an apology (you'll need to teach this at first), then tell her 'thank you' and hug & kiss. Be ready for her not to stay in T.O. the first time or two, but if you stay firm and return her to T.O. until she stays the ENTIRE 3 min., she'll learn YOU are in charge and will cooperate. My children still hate T.O.s but they know they must cooperate.
Regarding Daycare, I found the best practice was briefly explaining our T.O. process and asking Daycare workers to help in maintaining consistency while my children are at daycare. Daycares should support this (within reason, of course), since T.Os are an accepted form of correction for childcare centers.
Finally, as adoptive parents ourselves, we learned it's natural for many APs to feel less secure in the discipline techniques used - especially with the added "oversight" we endure more than birthparents. BUT, remember you ARE the parents, plus you've received more childcare training just to get approved for adoption, than 90% of birth parents. (This is NOT say in any way birth parents are less aware or educated...) Trust what you've learned and your natural parental instincts - adjust with your child's individual needs, and use discipline with love, caring and respect. Also, it's important to remain calm yourself while disciplining (even tho it's hard at times). If your child knows she can "trigger" you, she's learned a new trick!
Plus, I've found it's really helpful to connect with playgroup moms. If they have other (or older) children, they can offer a wealth of insight, support & ideas!
It's hard to set boundaries, especially at first (and as children change...), but it's important, and your child will be better for it and appreciate it as she gets older (so will you!). Best wishes!