Your idea will work, but the frequency accuracy derived will be no better than the frequency accuracy of the ATmega clock.
You don't want to introduce any other oscillators into the hardware.
The usual way to control a TXCO from GPS is to divide the 10Mhz down to 1 hz using a hardware frequency divider and to then input the divided down 1hz and the 1hz from the GPS into a hardware PLL, the output of which controls the TXCO.
This way , the txco has the same accuracy as the 1hz GPS reference.