You are facing the terrible twos. Toddlers at this age are indeed unable to vocalize all of their needs. It is a proper time to begin teaching her that she can't get everything she wants or you will hate parenting. Focus on her needs only. If you spoil her now she will be running you the rest of her life. It is much easier to set ground rules now than to change them later believe me! It can be a joy if done properly. You have to become a team with your husband so she doesn't get confused. Don't let her control either of you; after all she came to live with you and has to learn to live by your rules. A child feels more secure if she/he has boundaries and knows what to expect. She will be less frustrated. Time outs have to be used and changed according to age.
Time outs are for when she doesn't mind you or does bad things. Get down to her level calmly and explain why she has to go to time-out. If she leaves before her time is up take her back and again on her level tell her that the time is not yet up. As my kids got older I re-started the timer for the entire time. Praise her when she does it right, but not over praise. Let her know that you are happy that she did as you said. Have you ever watched Super Nanny? It is an excellent example of how to train and raise your precious little ones. I wish I had been able to watch a program like it when my kids were little. It would have saved us time and frustration. I learned more about raising/training kids when I taught.
Get on the same page with your hubby and then follow thru. I think he may be a bit tougher like all fathers tend to be.
Another thing that we always did was remember back when we were that age and how we felt about things. You always want open communication with your kids and if you tell stories them about things that you went thru at that age they will feel that they can come to you with their problems and concerns when they get older. Kids love stories so start now telling them about you and all of your family. My fondest memories are the ones when I sat listening to my Grandma. I learned so much about life.