For the splitting, I recommend not to use a splitter.
Instead, you can use a -10 or -20 dBm bi-directional coupler. You send the -10 dBm signal to the EOM amp, and you can fill up the needed power for the LO mixer. Also the "bi" nature of the coupler means that you can check for reflected power to diagnose if you are having impedance mis-match. Since you don't have an isolation amplifier in your setup, its important to make sure that reflections from one leg don't go back into the oscillator and disturb the other leg. Or maybe your oscillator box has an isolation amplifier between the oscillator and the splitter?