My Job Wants Me To Travel To 2nd Work Place With No Pay

I work at a veterinary clinic. We will have shifts for the weekends meaning arriving in the morning and evenings just to take care of the patients that are there and then leave (two employees). We have a 2nd clinic about 20 minutes away. With us being short staffed at both places, we are having to pick up extra shifts. Our job is wanting us to travel between both clinics to take care of the patients twice a day for Saturdays and Sundays. We are told to clock out to drive to the next clinic and then clock back in. Is this normal?

I understand traveling in your own vehicle on companys time but i dont feel like this is right being forced to two locations. TIA