Here's a simple solution for sharing a circuit where only one side is running at any time. Cost is about $100 for parts.
Get a double-pole, double-throw, 40A relay, with a 120v coil, for example this one:
http://www.grainger.com/Grainger/DAYTON-Power-Relay-5X847?Pid=search" onclick="window.open(this.href);return false;
Get a healthy-sized box to put it in, e.g.
http://www.homedepot.com/h_d1/N-5yc1v/R-100552487/h_d2/ProductDisplay?catalogId=10053&langId=-1&keyword=nema+3r&storeId=10051#specifications" onclick="window.open(this.href);return false;
Get a simple 120v timer.
Wire the 240v circuit through the relay, with one socket coming off the NO side of the relay, and the other socket off the NC side.
Wire a 120v socket off the supply side of the relay. Plug the timer into this, and wire the relay coil with a 120v plug that you connect to the timer output.
Set the timer to power the dryer during the day, and the car by night. Most of these simple timers have an override, so you can dry or charge anytime, and the timer will drop back into its normal settings within one cycle.