I wish you luck, but you have to state your cause. I will say you can not blame someone for something they are doing that is causing you stress if you never tell them (that is a quote from my daughter -- yes I taught her everything she know
).
This woman most likely does not have "money or budget" issues like many people do. It may never have occurred to her the stress the gas bill is causing you. You have to talk to them, if they don't correct it then it may be a time to look for another family... but at least you will know this time to not allow your car to be used.
Also.. while your at it... what about wear and tear? Tires, oil and repairs? Car insurance?