Hi R.,
I own North Tx Sitters based out of Keller but services NE Tarrant. We send out sitters for date nights, weekend sittings, week days etc... I do have some girls that do that nanny roll as well. I personally nanny 2-3 days a week.
I have ran a daycare with 300 kids and 45 employees and have over 15 years experience. I have researched many many hours on prices. A typical BABYSITTER makes $12-16 an hour while a nanny makes $15-20 an hour.
As these other moms are stating you are not paying her enough $10 and as Jennifer M stated I am surprised she is stating. I have 16 families in Southlake that pay an avg of 18 an hour for their sitters not nannies and they tip on top of that.
If I were you I would be happy to pay for her tires if that all she is asking.
To maybe avoid her asking in the future i would pay her the normal nanny rate for two children which is $17 an hour (15 first kid $2 per kid per hour after) and then she should not have the need to ask for tires for the future.
Also everyday she takes your children in her car she risks accidents which could go on her insurance which could be upped.
Southlake and Colleyville are the highest paid employer cities in tarrant county for nannies and sitters. I would take that into consideration as well.
HTH