Lydia thought to write in with a hack that I only discovered after my second child was almost too big to ride in the cart:
When going shopping various places with the little one, I always park next to a shopping cart return area so I can put her and her paraphernalia into a shopping cart asap. Also a plus, after our excursion I don't have to leave her long to put the cart back once I've buckled her back in the car. I always feel bad leaving the random cart in the parking lot for someone to collect, but I feel even worse leaving my daughter unattended in the car. I know I could just heft her around, but babies sure do know how to pack on the pounds fast!