On my way home, I dropped by my mother's. or On my way home, I dropped in on my mom. I'd love to come over one of these days. or I'd love to come over to visit/see/hang out/etc with you one of these days. The difference between the two is that the first one is saying what you did, the second is what you will/want to do.

The second sentence should read something like "I'd love to come over to your place one of these days". Both "come over" and "drop in" represent examples of phrasal verbs, and their meanings roughly coincide. "Drop in" implies a spontaneous, unplanned, perhaps unannounced visit. The British say "pop in". "Come over" implies to me the aspect of proximity. If your home were nearby, I might say "come over".

I agree with Richard and Randy. The phrase is 'drop in on' someone. You usually use it for an unplanned casual visit, when you are passing someone's home on your way to somewhere else, or when you happen to be in the vicinity of their home for some other reason.

The first sentence should be corrected thus: "On my way home, I dropped in AT my mother's house." In a more casual tone, you could write "On my way home, I dropped in TO SEE my friend." (or, "at my friend's house"). I sort of agree with Randy about the meaning of "drop in". It could mean "not agreed upon beforehand" and "unannounced" as in "I didn't tell you I was coming or, at least, I didn't tell you until shortly before I arrived". However, it's possible for me to say to a friend, "Why don't you drop in around 3pm Saturday afternoon?" Here, we agree that you're coming Saturday afternoon, we even agree on a time but there's sense of casualness and spontaneity. If I said, "Why don't you come over for dinner at 6pm Saturday evening?", that would be a more formal invitation where I expect you to arrive at 6pm. Another example..."While we're in London, let's drop in on our friend Steven." Here, there's still spontaneity and casual tone but it's clear that we're planning to see Steven significantly in advance of our arrival in London. It's unclear when we're going to tell Steven we're coming. Maybe we'll figure it out after we arrive in London based upon the other commitments in our schedule.