I understand how you feel. My son was just diagnosed with adhd as well and he is also 4. The first medication they gave him was horrible and it seemed to make him worse as it did in your daughter. The second one seemed to help a little better, however, now it seems to almost not have any effect. To help assist you though, I found out by trial and error that my son has an allergy to red dye that most children with some form of add or adhd do and let me tell you that was a godsend because he also had anger issues and was very destructive and we found out this was most of the cause.
You wouldn't think something so trivial as red dye would have such an impact on a child but it sure does. Not long after having it he would be so wound up and every little thing would throw him into a fit, sometimes it would be a fit of rage and destruction combined.
Now by my trial and error, I read on the internet, to take them off all the bad foods and give them only foods that come from nature for about 2 weeks. After that two weeks, slowly add in processed food and food with dyes. I didn't completely take him off everything as they suggested but I did take everything with red dye out and then one day, I gave him a strawberry yogurt. It only took about 30 minutes after for me to realize that this was the major source of his problem. Now don't get me wrong, this is not a cure by any means because he is still extremely hyper, however, we don't have quite the anger and destruction issues we had before. The fits and the temper tantrums have decreased alot compared to what they were before.
My child's father was diagnosed with adhd as a child and as an adult, he also it bi-polar and obsessive compulsive. Doctors will tell you 2 out of 3 of these aren't necessarily genetic and don't have much to do with your child's condition, however, you being in almost the same situation as I know firsthand that it probably does.
Anyhow, good luck to you and hopefully you will find that while it may not be a red dye allergy that's affecting your child, it may be some sort of food allergy you're not aware of.
I wish you all the best.