Hi Raun. I have no idea if you're still on Ancestry, but I'll take a chance. Your mom hasn't passed on your email so I can't contact you directly.
Anyway, I have been in contact with a 2nd or 3rd cousin in Australia, and between us, we have traced the Rainbow line back to Thomas in the 1700's. Your great-grandfather's name was Henry Thomas, not Frank. The Rainbows lived in or very close to London since the first records we have found. Henry T. seems to be the only one who left, except for Alfred B.'s daughter. Hence the Australia contact. I suspect that the other responses you have received were from a different line of Rainbows, altogether.
I hope you receive this. When you reply with your address, I can send you the entire history, if you like.

I hope to hear from you soon! Love, Aunt Edna.