Well, I wish you all the best since not even the HST can resolve any Apollo objects! They're way too small to be resolved even by its 2.4 diameter primary mirror. So unless you have something a few hundred times larger in your backyards, all you are going to see is the usual lunar selenological stuff.
Because of the bright moon - there is not enough contrast to resolve it, all you can expect is a microscopically different color on a 85 meters large pixel on the lunar surface.
But if you are not looking for an object on the surface, against the dark background, the contrast would be far more favorable. Next, if you collect enough data, instead of looking for a specific object, it would be enough to look for lines in a long-term picture of the lunar neighbourhood.
Yes, that shouldn't be enough to tell that we have found the LM. But it could be enough to catalog objects around the moon and look closer at them. The moon isn't that densely populated with satellites yet. Stars, NEOs and SpaceX sky pollution (tm) should only be annoying.
A night should be enough to detect 3-4 orbits of spacecraft in lunar orbit.