Do any microcontrollers allow steering of inputs to outputs?
For this purpose I would recommend the use of a USB 2.0 Multiplexer IC.

Many are available, a typical one that supports 480MBit USB is the Analog Devices ADG772...

http://www.mouser.com/ds/2/609/ADG772-878543.pdf

Or the Texas Instruments TPS65981

http://www.ti.com/lit/gpn/tps65981

There are many others though and the price range reflects the number of features available.  If you require Host or Device functionality will dictate some of the design requirements as will "OTG" and "dedicated charging".

Follow the datasheets' PCB layout recommendations for whichever chip you choose.