Motor Control with PMW or RPM on heavy robot
Your second problem is probably closely related to the first. When you write the calculation:

Left Wheel = ( FrontError - SideError ) * Acceleration


what you really mean is:

Left Motor Input = ( FrontError - SideError ) * Acceleration


If there is a significant difference between the input to the motor and what the wheel actually does, perhaps because there is an unexpected load on the robot, then it is going to be difficult or impossible to tune those FrontError and SideError PID controllers in combination. If the wheel response is not linear you cannot simply add together two PID outputs and expect to have both work at once.

You have two general solutions here -- either develop a model so you can compensate for the difference, or make it so that the wheels actually respond fairly linearly to their input. This second option is probably the best one and it is what you will get if you use encoders and separate well-tuned PID controllers for each wheel.

Depending on all the other variables involved, the latency may prevent your control system from being stable. A simple two-pole PID controller might not be able to compensate adequately for it, but if you're experimenting it would be worth a shot, especially if you can fix up your wheel drives.