Well, KB, you've got at least two choices. You can develop the way it breaks around those transition points, and go for the yodel/break effect. Or, to smooth those out, practice making like a fire siren. I'm serious, or at least the vocal coaches that said this were. Start as low as you can, do a big swooooooop up as loud as you can, and then come back down the same way.
Opening your throat really wide like a yawn, keeping your head level and pretending to scream helps get the high voice stronger. (It's harder to sing high quietly)
Do you know what it means to use your diaphragm when singing? If you do, do it!
Blessings,
Barbara