The week before my son turned 3 we moved his bed/crib out of our room. It sounds strange to some people but, I nursed him for 21 months so it was easier for all of us to be in the same room. I couldn't stand to listen to him cry it out. After that, he did 5 months in night braces on his legs. We never meant for him to be in our room that long, but it just sorta happened.
At the end of last summer we implemented a new bedtime routine. Brush teeth, read a few books, a prayer, hugs and kisses, goodnight. He would get upset and find excuses, but he started falling asleep in his bed, not ours, and on his own. He would get up 1-2 times a night where I would redirect him back to bed.
So in February right before his 3rd birthday we switched him into his own bedroom. We kept the same routine and were ready for the tears and the whining. He still has a hard time falling asleep on his own, especially when he is extra tired, but he knows we aren't giving in and relents. Most nights after rolling around for a bit he falls asleep. We have the video baby monitor up and he knows we can hear and see him even though he can't see us. He still wakes me up almost every night, but I steer him back to bed or catch him before he gets out. There are a few nights with tears, but not the uncontrollable tears, more like he's upset cause it's bedtime.
I would suggest trying out a whole new routine. When we did, I would tell him I would come back and check on him every few minutes (which I did) until he no longer needed the reassurance. Its not going to change overnight, but 3 is different than 3 months and you have to expected the resistance and tears. Once she sees you are sticking to your guns it will get better.
I have to say, I'm glad about not doing self soothing as a baby. I wore him in a baby wrap alot and he was the happiest. He never really cried and he became independant as soon as he could walk. He has good social skills and apart from the sleeping never really had other normal fears or seperation anxiety. Most parents who say their kids sleep through the night are untruthful (check the studies), and quite a few mom use it as a competition. Don't second guess what you did prior, because you have to know you did what's right for her then and you are doing what's right for her now. Happy Slumber!