If your son-in-law is 'at home doing chores' then it is his responsibility to get the children to their class. If he is working from home that is a different situation, but even so he should be able to negotiate a one-off absence for child -care.
Your oldest daughter is ridiculous in describing an alteration to her child-care arrangements as emotional abuse when all she is suffering is a minor inconvenience.
It sounds as though the arrival of your youngest daughter on the scene is already causing family discord; perhaps her siblings have suffered from this in the past which is making them so resentful now.
Your middle daughter needs to learn to drive, unless there are particular reasons why she can't, or won't.
You need to move out of your daughter's home as quickly as is convenient for you, but all three daughters, and spouses, need to be reminded gently but firmly that you are not simply cheap child care.