You will only get interrupts from the PWM port in case you have enabled them. If you have written your program in a good way, all calculations are done before you receive the PWM interrupt and the only thing that you need to do upon reception is to copy down the new values into the PWM registers.
If you keep doing things during the reception of data from the SCI, you need to make sure you finish it before the next byte is sent. For example if you are running on 9600, you have 1/9600 * 10 bytes = 1ms as a minimum time before the next byte is expected.
If you want to let a lot of code run when an interrupt is triggered, but you worry about other processes that are running simultaneously, then 1) disable the interrupt source, 2) enable interrupts with CLI. Then you allow other interrupts to take precedence.
You can also set the HPRIO register to point at the most important interrupt, to avoid some code gitter. If several interrupts occur at once, the S12 will pick the one with the highest priority and the others will have to wait.