light travels at about 30cm/nS. The Uno can capture +/- 1μS at best, so, at best, your accuracy will be +/- 30m.
In the nRF24 library I'm using, there timeouts, meaning that you will never know exactly how many μS a network.read() will take, adding multiples of 30m to the best case.
+/-2m is not possible using an Uno and any radio.
Try two GPS's, one on each module with each Nano and take the difference between the two. I'm pretty sure that would meet your spec. (Amazon) Yes, one GPS is rather inaccurate, but the inaccuracy is the same on two relatively close (google "differential GPS") That would be a cool project! And! you could log the track! You can find less expensive modules on AliExpress (caveat emptor and 20-90 days delivery)