It depends on your area J.. I am in Plano/Allen area. My 16 yr old averages $12-$15 an hour which is very generous. Believe me, she foregoes her date nights on weekends for a specific 2 families if they ask her to babysit.
My daughter would have been ok with the $50. It is not like your 2 children were infants... they are somewhat self sufficient and just need proper supervision. It would be different if they were both in diapers, bottle fed and put to bed, etc.
When we had sitters for our daughter, we guaranteed $40 for the night, even if we cancelled for some reason and then added to that. Our weekly date nights were always $60-$80 cash. We were usually longer than 4 hours.
Don't fret about it either way. One mom showed up at my door to pay daughter an extra $20 because she felt like she underpaid for her 3 girls. my daughter said, don't worry about it, it all evens out... just call me the next time.
My daughter is CPR trained, she does interact with the children by teaching them Spanish. SHe is in AP Spanish 4, parents love for their children to learn it, my daughter gets practice, great both ways. She also does mani/pedis for girls if mom's approve. She takes books, puzzles or things the children might like to play with that is different.