I ran Family Daycare before having my babies and can tell you this is completely normal behaviour - especially with the TT regression. There are only a few things in an older toddler/early pre-schoolers life they have control over - and TT is one of them!

Nappies are probably not a great idea, unless DD hates them.....or you don't mind starting all over again.

As for the tantrums, they are at an age where they are entirely ego-centric and can't (even if they wanted to) see outside of what they are feeling within themselves. This is why their reactions over the smallest things seem so over the top and hard for an adult to understand.

It's great that you encourage talking after the meltdown - keep up with that. Also respect that she is probably feeling frustrated, angry, tired, sad (whatever the case may be) and her only way of dealing with these emotions are emotional outbursts.

As she gets older you can try some control tactics - in that you give her a few tricks to try when she feels herself losing control. But for the minute my best advice is to ride the wave