1 hr commute sounds like a GOLD MINE for studying. Agree with all the suggestions for audio lectures.
For board study, I gave up studying at home and spent the $ to go to a hotel for a weekend and watch an online board review course. Cheaper than attending in person as split the videos with co-residents.
Instead of framing child care as help for your parents (who might take it as criticism of their abilities) can you frame it as socialization for your child? Many cities have drop off programs or classes (my 3 yr old took a cooking class) that give caregivers a break. Community centers in my area have cheapest options.