Using RF for relative direction finding for short ranges (sub 10m)
The most effective antennas rely on the length of the "parts" being a defined sub-fraction of the wavelength of the signal that is to be received. This is usually a quarter wavelength (dipoles) for both halves or juts a quarter wavelength for a one-ended dipole (aka a quarter wave dipole).

Yagi antennas use other fractions to define the length of the reflector, driven element and directors.

Parabolic dishes become more directional and have increased gain as frequency rises but these will need to be big to get the directionality I think you need.

In short, I think you may be fighting some of the laws of physics.

Some good news - you won't be needing more than a milliwatt given the distances you are talking about.