Do you think this board can be done in 2-layer or should I go to 4-layer?
The way to handle the analog part is not to split the ground plane (this increases its impedance, which you want to avoid) but to isolate the components and sensitive signal traces so that the analog signals (and their return currents in the ground plane) do not cross other signal paths.

That said, if you're worried about signal integrity or noise (IMHO, that's "yes" for test equipment like an ohmmeter--nothing worse than an instrument that lies to you), go with a 4-layer board. It'll be both easier to route and have better signal quality (Note that with 2-layer, the ground return path is via traces, so if you make the return current go all over the place, your ground will bounce, and there will be no way to repair it.) The most expensive board is the one that doesn't work.