I am not aware of any sound card that supports different sample rates on I/O, which IMHO is technically near impossible. If at all then by onboard sample rate conversion on either in or out, and not from RME.

The Mutec is neither a soundcard nor an interface nor handles audio. It's not what you asked for. You would need at least two interfaces/soundcards to work with different sample rates simultaneously.

I know FL Studio can have two instances open at the same time, so you could have one working as your main set to one sample rate and another at a different sample rate and use the rme mixer to join the two.
I have used it this way when i have a large project that needs the highest buffer but want to record at the lowest buffer, its not perfect but it works.
I've considered getting an rme hdsp card to go along with my fireface for perhaps better performance.

I'm not sure what daws you can open two of, cubase cant because of the dongle, but others may.

Not sure as to whether or not they support Linux, but...
Lynx Studio AES16e-SRC and AES16e-50 both utilize the very good Texas Instruments (Burr Brown) SCR4392 asynchronous sample rate converters on the inputs (the -50 version adds AES50 I/O via an internal connector, but is otherwise similar to the -SRC version). Utilizing that asynchronous sample rate converter functionality would allow a different sample rate at the input port and output port by converting the sample rate of the input stream to the different sample rate used internally, and the internal sample rate is what is used on the output.

The biggest downside is that these are not RME products with RME's excellent drivers, support, and the very capable TotalMix.

Here is some information about the SRC4392, which is very good at what it does.
TI product page: http://www.ti.com/product/SRC4392
TI data sheet, pdf: http://www.ti.com/lit/gpn/src4392
Additional info related to the evaluation module: http://www.ti.com/lit/pdf/sbou038