Definitely justified, especially since you're teaching and not just babysitting. I would also discuss compensation for travel to work and on outings.
How old are they? If they're still at an appropriate age for time out, I say you gather them together, explain the rules to them. Once they know the rules and you expectations of how they should act, if they break rules, they get one warning. Be sure to... more
My regular rate is typically $15/hr + $2/hr for each additional child. For special needs children, particularly due to my experience, I charge $20/hr as a base rate. Due to your education and experience, I would say you could probably charge $22-$25/hr
The Care.com Community is an advice-sharing network for parents and caregivers.