Did you build this house yourself or is it one that came with the town or possibly even one you downloaded? If you didn't build it yourself, I have an idea that might work:
Step 1: If it's an original house: Start a
new game in that town, find the house in the town and save it to your bin. Return to the main menu. If you downloaded it, go directly to step 2.
Step 2: Load your save. Go into build mode, and place everything in your family inventory. Especially things like trophies and skill certificates as those are
irreplaceable.
Step 3: Go to Edit Town, and evict the family. This will place them on your clipboard in the upper left hand corner of your screen. When this is done, demolish the house.
Step 4: Go to your bin and place the copy of the house from your bin on the now empty lot. Make sure it's positioned correctly.
Step 5: Click on the sims on your clipboard and move them into the house. On the off chance that they can't afford it, press CTRL+Shift+C and enter "freerealestate" without quotation marks before you do.
Step 6: Refurnish the house from your family inventory, sell anything that you don't need, and continue with life as usual...hopefully minus the pesky ghost.
If you're concerned with the integrity of your game (i.e. don't want to cheat to get money), simply jot down the current family funds before you evict them. Once your ghost problems are solved, press CTRL+Shift+C and enter "testingcheatsenabled true." Press CTRL+Shift+C again and enter "familyfunds Name #" only in place of "Name" type the family's name, and in place of # you type the number you wrote down. For example if their name is Smith, and they have 1,000 in their coffers, you type: familyfunds Smith 1000. It will be as though the entire ordeal was just a bad dream.
If you built the house yourself, try evicting the family and then go into the house in build mode and see if you can remove the ghost that way. It's possible that the act of evicting the family might even eliminate the ghost, so you could simply return to edit town and move them right back in with no additional effort. If not, save the house to your bin and place it on the same size lot in a new town after exiting without saving to see if maybe that jars it loose. Other than that, all I can suggest is that you recreate the house in a fresh game as best you can, save it to your bin and proceed as I described above.
And to answer your other question: If you change active families, you won't lose your relationships per se. Story progression will take over, and those relationships will change, going up or down as dictated by the game. They might even meet new people. Just keep in mind that there is also a possibility that bad things will happen. Sims might die, marriages might end, babies might be born (that could be good or bad) and they might change jobs or just get fired/quit. The only thing that you will not keep are any short term wishes you have "promised." So complete any big ones before you switch.