Recently, my employer has made on-call/standby for overnight and weekends mandatory. Up until this point, on-call/standby time has been completely voluntary. I have two problems with this proposed policy. Problem number one is, I am a single parent with a 9-month old child who has no one to watch him after 5 p.m. during the week and no one whatsoever to watch him every other weekend. This leaves me with 4 days out of the month when I am not obligated to babysit my child, yet my employer is telling me that if I don't go on-call when they delegate me to do so, I will be terminated. Secondly, my employer has a policy which states that anyone who resides more than 11 miles from the workplace is not allowed to drive a company vehicle home when on-call. I live 15 miles outside of said boundary, yet they are trying to force me to take calls using my own fuel and causing wear and tear to my own personal vehicle. My question is, are either of these things legal for them to do?

Both of them are completely legal.

This will sound harsher than I mean it to, but your child care issues are not your employer's problem. Outside of FMLA, and child care does not fall under FMLA, your employer has no legal obligation to take your family obligations into consideration. No law prohibits him from scheduling you for the hours he needs you or wants you to work, regardless of whether you have child care for that time or not.

No law in any state requires them to provide you with a company vehicle regardless of where you live.