Periodically, need to transport two children, one in front facing seat; the other in rear facing seat. Current car, Toyota Corolla, cannot accommodate both at the same time.
Budget is limited and job requires driving all day, so mileage is important.
It is not clear why you cannot accommodate both at the same time. Are the two child seats too wide for the rear seat, or do you push the front seats too far back, or some other reason? Your description will help us advise you on a more suitable car.
How about a mid to full size sedan? Not only do they have plently of room, many models are very comfortable and get decent mileage. Examples you can buy fairly cheaply include the Ford Crown Victoria/Mercury Grand Marquis, Chevy Impala, Hyundai Sonata, Toyota Camry, Honda Accord, Chrysler Sebring, the list goes on.
A small SUV or minivan would also be suitable. Really, most cars would meet your requirements… I’m surprised the Corolla doesn’t.