Since you can make multiple nannies with this mod, I'd assume that the mod only affects nanny creation, not how they act afterward.  Since you're the only one with this problem, I suspect that  you've got another nanny mod causing problems.

Things you can test: (You can stop once the nanny doesn't get stuck.)
1) In the neighborhood with the custom nanny, play a house that uses the elderly nanny, if you still have one.  Does she get stuck in her car too? 
2) Back up the neighborhood.  Kill off the custom nannies.  Hire a new one, who should be elderly.  Does she get stuck in her car too?
3) In an empty neighborhood, make a CAS family with a toddler.  Hire a nanny.  Does she get stuck in her car too?
4) Navigate to My Documents/EA Games/.  Rename The Sims 2 to something else.  Run the game.  Repeat step 3.  When finished, delete the new The Sims 2 and rename your old file back to The Sims 2.

If the nanny gets stuck in step 4, your games files have been corrupted and you need to reinstall.  Sorry!
If the nanny isn't stuck in step 4 but is in step 3, you've got another nanny affecting hack.  Try HCDU or a binary-divide-and-conquer.
If the nanny isn't stuck in step 3 but is in step 2, something in your neighborhood is corrupt.  There are several candidates, but I'm not sure what to recommend.
Step 1 and step 2 should have the same results (stuck or not stuck).  If not stuck, you're done; your game is fixed.

Didn't realize  you'd moved, new boards look good!

I'm not sure what an interior foundation is... but here's my best guesses:

1) If you want a foundation wall on the floor above the basement/foundation level, use a regular wall, save and quit the game, and use Mootilda's Wall  utility from MTS to make it a foundation wall.

2) If you're making a double wall foundation on the same level to hide the sloping grassy bits, use a regular wall on the inside.

Try  http://www.box.com/shared/3k3sz9ntf7

Do you have any other hacks that affect marriage or relationships?  Try HCDU from http://www.simwardrobe.com to make sure.

If  you've got a lot of mismatched outfits and icons, you  might want to delete your Thumbnails folder and allow the game to regenerate them.

Try using "move_objects on" to delete the sale signs.

Depends.  (It would be nice if you could find out what the creator's wishes are, but we're assuming the creator has dropped off the end of the earth too.)

If it's a mesh and you really want to make a new texture for it, yes, include the mesh.  I've had this happen; I made recolors for the "turtle" sweater from 2-f0r-u, then discovered the site had vanished.  Wasn't a particularly well made mesh, but I liked the style...

If it's a hack, NO, do not distribute that hack in any way unless you're willing to take over supporting it as well.

If the creator's TOU says they don't care, go for it, just specify "created by So-and-so" to prevent people thinking the files are your creations.

Otherwise, yeah, let them vanish.

Really stupid thought: Is there a menu item that also has that functionality?  Accelerator keys usually have a corresponding menu item.

We have other threads about how to find the FrannySims downloads.  Consensus is that they're pretty much gone and you need to find a recolor download that includes the mesh.

If the sexyfeet mesh is intended to replace the blockfoot version, you only want one.  You need to realistically consider if your computer can handle the extra polygons in the sexyfeet mesh as well as if you've downloaded any skintones that have shoes painted on the nude mesh.

I'm very confused... the head and body are supposed to be separate parts.  But I'm sure you'll figure this out from the tutorials Theraven sent you to.

You can also use CleanInstaller to remove the skintone and/or meshes from the package file, which will shrink it hugely, btw, and specify in bold print in your post that they need to download the skintone and give the link.

Doesn't help much in your specific case, since you've linked it to another mesh, so it's not available as a separate download.

Stupid question, did  you check jwilson5's area to see if she already has the skintone linked to that mesh?

If you have DD, as well as checking My Documents/EA Games/The Sims 2, you also need to check My Documents/EA Games/The Sims 2 Double Delux.  Stupid but true!

If  you have very many downloads, you might be better served with a full fledged Binary Divide and Conquer instead of the 50 at a time method.

Does  your game run?
Have you used SimSurgery to extract any Sims from  your game?