Ignoring is a very important teaching phase. Our whole family takes it very seriously when ALL the kids-30 cousins included-go through it. It is disciplined like any other major rule. One calm warning to listen, and respond, and a consequence if you've had to repeat yourself more than once or twice. You take action way before you would become annoyed or angry. It always works, the kids always learn, the phase is really brief.
A good idea when someone asks something of the child (if it's you, or someone else asks your daughter something but she ignores them), you walk up to her right away, make some physical contact with the second warning, like place a hand on her shoulder and say, "Junior, ANSWER." This lets them know you are totally focused on them and a consequence is next if they do not respond. My kids ignored me a few times around age 3, but soon learned it was a major rule not to ignore mom. Sometimes they (well actually I) slack, but when I give the last warning, they know it and hop to.
The catch here is if you will feel OK since your daughter is newly adopted. I think ignoring or walking away in any case is negligent parenting, but many people feel differently. My brother and I were both adopted, and our parents didn't sugar coat things for us, thank goodness, we didn't spend countless hours wallowing in time outs and power struggles or getting ignored. If she was not adopted, how would you handle this? Keep in mind that even if she was your blood relation she would still do the exact same thing. She is now your real daughter, you should treat her as such. It's not mean to teach her respectful behavior, and it does not mean you do not unconditionally love her. The opposite is true. Love includes discipline and teaching respect. Keep it brief and clear so you can get back to having fun.