Correct way to convert square signal to sine waveform
Is this correct or may be exists more correct or easier solutions?


DDS is probably a good way. The AD9837 is one of the simpler devices to use and because of its flexibility I'm suggesting it.

It can generate sine waveforms of the frequency you require with ease and it is programmable so that these waveforms can be changed on the fly. In fact for your application it neds to be programmable because your modulation signal needs to control the device by an SPI bus probably using a small microcontroller. I'm aware that you are not an electrical engineer so this solution may not be the most convenient but, if you are looking for flexibility and accuracy I think this is probably the best solution.

On a slightly different note, you are proposing, for say a 1, 0 sequence, 2 cycles of 200kHz followed by one cycle of 100kHz - I would have the changeover at the peak of the waveform in order to minimize harmonic disturbances: -



The red circle indicates the point where the waveform switches from one frequency to another and this will give rise to more harmonics than switching at the peak of the waveform as shown in the lower diagram.

This of course means less filtering. Either method can be done with DDS.