I can't offer much advice and maybe you've already solved your issue, but almost any microcontroller will be capable enough to address this task. Ideally one with ADC (to read in the signal from a presumably analogue accelerometer) and a serial module built in (so you don't have to code that stuff yourself) for sending the info to the vehicle. Yes, a range of acceleration, steering would be easy - not really any more difficult than just having forwards/backwards.
For example I'm using the generously sized PIC 18F4520 - its MSSP (serial module - both SPI and I2C protocols) is straightforward to use, as are its ADCs. Code snippets and libraries are available everywhere, free C compiler (C18), development environment etc... PICs are all I know, but are popular for a reason.
Just today I got an 3-axis accelerometer from Sparkfun, they have several. A 2 axis one would suffice for your purposes.
As for radio stuff. You'll need an encoder/decoder with a modest number of channels (one for steering, one for acceleration etc.) - LINX is often mentioned but I'm sure there are many others. As for receiver/transmitter I'm currently playing with 433MHz stuff from a robotics store.
If you're starting from scratch it might be a long road, but I started with an ambitious project and eventually it succeeded. Good luck.