Will the 1 1/4 hose be sufficient for the motor as well as chiller or should an auxillary be run. What's the best way to plumb the system

Yea, the 1.25" is adequate, but the drive's pickup is not. I'd add a second transom pickup to supply the engine and use the drive to supply the chiller. This way the chiller will only see water flow when the boat is moving.

Leave the stock water system to cool the motor. Get a separate water pickup and mount it on the transom. Run the water thru a sea strainer and then to the chiller. The run the output of the chiller to a water dump on the back of the boat. You only want water going thru the chiller while you are moving (on plane). I run my Whipple this way with very good results.

I have a 1 1/4 thru hull pickup that's unrestricted unlike the gimbal assembly, which I use for engine cooling . The drive has low water pickups which are unused except for cooling the drive passage to the hose. I was going to add a 1/2 bung on the strainer to feed the chiller which would have a press. relief and dump over board. I was also contemplating teeing into the 1 1/4 thru hull with the low water pickups incase flow wasn't good enough