If you really NEED to do 2 or more tasks at the SAME time, you aren't looking at an Arduino or a PSoC. In fact, from a PC point of view, you would need a multi-core processor with a core per task. OR... You do the thing in parallel hardware. The average CPLD (Complex Programmable Logic Device) can easily work on many concurrent tasks and the FPGA, well, they can do anything. If you can imagine it, the FPGA will probably do it. For a programmer, the most difficult thing about the transition to CPLDs or FPGA is the fact that EVERYTHING happens at the same time. A task may be in a Do Nothing state but that condition is sampled (usually) on every clock and there can be a whole bunch of tasks. All merrily doing their little bit or waiting for a wake up call.
What usually happens with a microcontroller is that we either write a 'super loop' that does bits and pieces of each task or we use an RTOS (Real Time Operating System) to divide up the processing power in some kind of priority scheme. For the project, as described to date, a microcontroller with a timer that can connect to an output pin is probably all it takes. Internally, this is hardware with the clock frequencies controlled by setting the timer register. BTW, generate double the desired frequency so you can square it up with a flip-flop on the output. For example, if you need to divide by 38, divide by 19 instead and divide by two with the external flop.
The problem with discussing this project is that only one small aspect has been described. Create two carrier frequencies and switch between them. An oscillator and some counter chips ought to do it. But that isn't the project. Now there is a discussion of modulating the carrier. That's an entirely different question. Regardless of the application, where does the modulating frequency come from? Does the <solution> have to create it? And so on... It's pretty easy to underspecify the project, follow a path down a rat hole and then find out that you simply can't get there from here.