Sorry, I lost the OP by hitting mark all read. The OP has 1 timer for both
sprinkler zones and drip irrigation zones, and wants the drip zones to work
even if the rain switch overrides the system.

If you have a spare wire to the manifolds where drip valves are, you can use
this spare as the common for the drip zones and connect directly to the common
on the controller instead of the switched common which is disabled by the rain
switch.