What's the Name of That Book??? discussion

This topic is about
Suddenly Twins!
SOLVED: Children's/YA
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SOLVED. Children's fantasy - parallel earth with magic replacing science & gender-swapped equivalents of people. [s]
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It's the "Magical States of America" books by John Peel. The first one is called Suddenly Twins! and the second book is the one with the magic carpet cover I remember:

And here is the Wheel of Fortune part in Suddenly Twins!, from google books:
The contestants were doing something to a huge wheel. Wheel of Misfortune, Chris explained. "The contestants have to outspell each other to win. I guess it's all new to you, huh?"
"We have something like it," Chrissie admitted. On this show, though, there was a Victor White, in a really ornate suit, turning letters on the board by snapping his fingers.
The weirdest thing is that I know this author from his Doctor Who books, and this thing I vaguely remembered every so often for years was by him. Wow. Can't believe I finally got it.

Books mentioned in this topic
Suddenly Twins! (other topics)Twice the Trouble! (other topics)
A detail I remember vividly is that when they're comparing the opposite-gender celebrities, the real world twin talks about watching Wheel of Fortune, and the magic world twin gives the name of the man who fills in the letters on their version of the show (like "Victor White" or something instead of Vanna White). At the time, I had never seen or heard of Wheel of Fortune, so it confused me.
I can't recall any other details about the plot or how the characters cross between worlds. I have a feeling it may have been part of a series and I believe that the cover was orange or red with an inset illustration of the main characters... flying on a magic carpet or something like that? Not quite sure. I also vaguely recall an "eccentric uncle" type character but again, not positive.
Thanks in advance for any help :)