Hi, my dd started working these in her developmental class early last year. Pretty much they taught the parts all differently, then put it all together with a spot. ( i mean, a station for going up into handstand, a station for coming back to straddle, on the beam, off the beam, etc) Now she is like your dd, 7 and a level 4. They mostly work these in their TOPs training. I think the key to doing two or more in a row is how they control returning to the straddle from handstand. (that just seems to be where the girls lose their balance and fall out of it) My dd practices handstand to straddle a LOT, and then goes for the multiple presses. She can do about 5 in a row now, if she keeps her focus on the "returning to straddle" phase.
I don't know if that even made sense, but I hope it helped a little...