When my wife and I went through a similar process, we used the online Church directory as the first verifier. Once things appeared correctly there, we then made sure the Tools app reflected that as well. Besides the data refresh, Tools will often have a delay (perhaps even more than a day), in syncing information that may already appear online. And there's rare but reported times where members struggle to get data to show up on the Tools app. So we tried to avoid using Tools as the first step in determining if things were "correct" or not.
If you go to the online directory, the drop-down at the upper-left corner will show the stake(s) your records belong to. Depending on what you see in the drop-down, that can also help indicate what still needs to be addressed.
Of course, the "Directory" tile in the Tools app also shows the stake(s) your records belong to. You stated Tools doesn't show you being in your home or the other stake. What do you see when you go to this Directory tile in your Tools app -- is it blank or show something else?