They're not going to work independently after connecting them together, that kinda goes without saying and is like trying to get water in or out of a garden hose after connecting the ends together.

You need to have that third button that makes RT and RB isolated from the other 2 that are just RT or RB. I'm sure the next question is how, so let's see...
Ya could use a DPST type of switch. It's only one button, but has 2 independent switches so they can't get mixed up. This would be the easiest thing to do, provided ya can find a DPST push button switch small (and cheap) enough.
You could use a 4066 Quad Bi-Lateral switch. Since it has 4 SPST switches in it that could be wired up to work like a DPST, 2 of them actually so ya could have another button do some other 1 for 2 kinda deal.
Ya could ditch the two 555 chips and go with a PIC, PICAXE etc., then ya would have to program it.