I changed Breezehome's navmesh in my mod. I want to delete my alteration and return to the vanilla mesh. How do I do this? Also should I delete my door linking into Breezehome and redo it?

if you have tes5edit, easiest way is to open cells..>..temporary your cell, there you'll see the navmesh entry. select that, delete it (this does NOT delete vanilla nm, just your changed version)
if you have no other modified or own navmeshes at all than this in your mod, also delete "navmesh info map" (the whole branch), close & save.

The easiest way is with TESVedit, but you can do it cleanly with the CK: NINJD by s7o

Load the Breezehome cell in your plugin and delete the navmesh. (Ordinarily it's a horrible idea to delete vanilla references, just stay with me here.)

Save your plugin and exit the CK.

Launch the CK and find your mod in the list of plugins, select it and hit details. Find the navmesh edits and you should see your deleted references. Select them and hit delete and save. They should be flagged as ignored.

Reload your plugin, load the Breezehome cell, and you should not see any star by the navmesh, as it should have reverted to vanilla. Save again for good measure.

Open in TES5Edit, then delete the NAVM (overrides) in Breezehome along with any inadvertent NAVM edits in Whiterun. I'd also remove the Navigational Mesh Info Map group before saving, opening in CK, finalizing the NavMesh, and saving. Your additional door's presence, if linked to another cell, will necessitate an override to the vanilla NavMesh, but should be updated automatically when the NAVM it's on is finalized

It might be prudent to completely avoid altering the NavMesh by using a scripted activator to serve as a fake door.

Please elaborate.

If you script an activator to teleport the player/activate followers and use MoveTo, you can simulate a door without having to touch the vanilla NavMesh. Adding a real door connected to another cell would necessarily add teleport data to the NAVMs/Doors/NAVI, making for NAVM overrides which, for that particular cell, seem to be problematic.