I want to make sure i hook this circuit up the right way. The datasheet shows the schematic, but doesn't tell me how to calculate R1-R4. If you go to page 6 figure 11 on the link bellow you'll see what I'm trying to do. I'm guessing that R2 and R4 are pull up resistors and should be in the neighborhood of 10K? And R1 and R3 are current limiting? Also if you look at figure 13, what do Rs and Rf do? voltage divider to trigger the backup at a different time?
Rs and Rf provide positive feedback to ensure there is hysterysis - this prevents oscillation when the supply is close to the battery voltage. Rf would be much greater than Rs. Rs has to be low enough to allow enough current to flow to the outputs, so something like 10ohm might do, Rf perhaps 500 to 1000 ohms. If the supply voltage is always larger than the battery voltage (except when the power fails) then the hysterysis circuit is not needed. If the circuit is switching between two batteries then it probably is required.
The other resistors are basically as you say - the current limiting resistors must be low enough to guarantee saturation o the PNP switches, and the others ensure fast and thorough switch-off of these transistors. They can all be the same value for simplicity - value depends on the current needed to saturate the transistors at full load.
Why not simply use a couple of diodes acting as an OR gate. Whichever system (primary supply or back-up battery) is the higher voltage will feed your load with the diodes preventing back-flow into the lower system voltage.
A----------D1-------I I I------------Load I B----------D2-------I