The title Cloud 9 comes from the old expression "on cloud nine," which refers to a place of total mental fulfillment and happiness. You might be on cloud nine if you just won the lottery, got engaged, or found yourself with miraculous, legitimate flu symptoms on the day of a big test that you "forgot" to study for.
In this play, Churchill seems to be playing with the idea of cloud nine as a happy place, brought about by the most fortunate circumstances. The problem is that some characters mistakenly think that everyone should want the same thing: a nice, traditional family. And of course, not everyone has the same definition of cloud nine.
For Edward in Act 1, cloud nine has something to do with playing with a dolly and (eew, eew) spending quality time with Harry. For Betty in Act 1, cloud nine has something to do with having a traditionally spotless nuclear family and also (less eew) spending time with Harry. So yeah, people have different ideas of happiness.
Churchill more or less makes this point clear at the end of Act 2, Scene 3, which ends with a song called (yup) "Cloud 9." The lyrics of the song basically lay out the idea that people have different ideas about what brings happiness in life, as you can find in lines like:
"Who did she meet on her first blind date?/ The guys were no surprise but the lady was great. They were women in love, they were on Cloud 9." (2.3.156-158).
Betty would not find this sort of situation conducive to landing on cloud nine.
One of the funny things about this song is that Churchill tends to put lines like the above next to corny, traditional love lyrics like, "He said be mine and you're on Cloud 9" (2.3.150). But here again, the joke's on us, because we probably just assume that the singer of the song is a woman if she's singing about going on a date with a man. It could, though, be a man singing about going on a date with a man.
And that idea would definitely put Clive and (Act 1) Betty into a tizzy.