You sound like you are setting boundaries and enforcing consequences, and that is what a good parent does. You don't sound intimidated by tantrums. Keep holding the line!
One thing that I did to make the time out chair work was to start the time out when they stayed in the chair. If they got out, time started again. This works with ages 4 and up--not the really little ones. I would stand right next to the chair with my timer. It does take a bit for them to understand that each and every time that they get out of the chair, the time starts over. EACH AND EVERY TIME. It was a battle that I chose to pursue.
I also did that with time outs in their rooms. When they were actively throwing a tantrum, it meant that they were not calming themselves. Teaching the child to self-calm is one of the main reasons for sending them to their room in the first place. Time started when they were working on calming--which did not include kicking doors. (Although, we had a few dented doors until they caught on!)
One thing that I did was put a preferred toy in time out. The toy was up on a shelf in the closet for s specified time. This was VERY effective. If they were trying to climb the closet, the timer was not running.
Don't forget that consequences can also be good things that happen because of positive behavior. Catch your child being good. Have positive strokes for her when she is doing the right thing. It doesn't have to be anything dramatic--just if she is doing what she is supposed to, praise her. Let her do something special with you. Give her a little treat. It is a lot easier to encourage positive behavior!