If Mars orbited the Earth how distant would it have to be to cause the same tides?
The Tidal acceleration between 2 bodies is calculated with this formula:

$$
a_T = \frac{2GM_MR_1}{Dm^3}
$$

Where $M_M$ is Mar's mass, $R_1$ Earth Radius and $D_m$ the distance to the Moon. If you equal this to Moon's Tidal acceleration you will get $D_M$ as distance to Mars to get the same Tidal acceleration having $\frac{M_M}{M_m}=8.73328184501$:

$$
D_M = \sqrt[3]{8.73}D_m\simeq2.06Dm
$$