We helped manage our friend's properties. She used our vehicle, which we also use for our other self-employment business. Can we deduct mileage here again?

Depends.  Did you get paid for the management of your friends' property?  If so, then yes, you can deduct the mileage for this additional self-employed activity, just be sure you are counting the miles separately and NOT deducting the same miles for each activity.  

The miles not related to the first business cannot be deducted on the first businesses return.

The mileage needs to be deducted and allocated to the businesses they were used for.