No need to add more relays...
The circuit is complicated enough already.
I don't know what's going on there, but it seems like you're losing some voltage from the passenger's side switch or something when it's all hooked up.
It could be a connector issue.
I don't know what type of connectors you're using, but make sure all the connections are secure.
If you had a voltmeter, you'd probably have it fixed already.
You need to check the voltages at the wires that go to pins 86 on R3 and R4 (when they are unhooked from the relays) while the passenger's switch is being activated.
Compare that to the voltages at those same points while the driver's side passenger switch is being activated.
They should be the same (or REALLY darn close).
If the voltages are the same, then it may be a current delivery issue.
Make sure you're using thick enough wire on those two jumpers (The tan and dark blue ones).
Since those two switches are wired together in parallel, they should be providing the very same function in the circuit.
Since they are not doing that, something's goofed up somewhere.
The only other thing I can think of is if there's an issue with where the 12V is coming from going to each switch.
It would probably be best if both switches were getting 12V from the exact same place, and that that place was different from where the relays are getting their 12V.
(Unless, of course, they are all getting 12V directly from the battery)
That's all I got, man.
It's hard to trouble shoot your stuff from here.
Let us know what you find.