Many mothers offered specific suggestions for the diaper situation that you might find very helpful, but it sounds to me like you're dealing with these tantrums constantly.
My daughter turns 2 next week, and I swear she hit the terrible twos the day she started walking at 10.5 months. What has worked really REALLY well for me is to offer her choices. I know, you hear this all the time - give them as many choices as possible like "the red one or the blue one?" I do that too, but what I'm suggesting goes a step further.
When my daughter decides to throw a tantrum, I offer her two acceptable options: "Would you like to stay here and be sweet with mommy, or would you like to go to your room to cry?" A lot of times I will lead into it with a "I know you are very upset, and sometimes when I'm upset it makes me feel better to cry, but mommy doesn't like to listen to you cry." I want her to know that her feelings are okay, but the BEHAVIOR is not.
When we first started this, she would just continue to scream, so I would (gently) take her by the hand with a comment along the lines of "Okay, lets go cry in Mia's room," and then lead her there. I would lay her down in her bed, calmly give her her pacifier and offer a hug and a kiss. I always ALWAYS tell her "I love you, please come out for another hug when you're ready to be sweet!" And then I left. Of course in the begining she'd hop up and come chasing me (still screaming) so I'd offer the choice once again, and repeat the process. She figured it out after maybe 4 times.
Now when I see a tantrum coming, I offer hugs first, tell her it's okay to be upset and ask her if she'd like to stay sweet with me or go cry for a minute. USUALLY she'll pick one or the other (it's so adorable when she chooses to go to her room. she pouts the whole way, cries for about 30 seconds and returns). Sometimes I have to go back to the "lets go cry in Mia's room" but the tantrums are far fewer now than before.
For more great hints, I HIGHLY recommend "Parenting with Love and Logic by Cline and Fay."
The happiest toddler on the block was pretty good too, it gave me a great understanding of where my daughter is coming from. However I found the todlereese to be bizarre, and never worked with my daughter...