I don't have Oasis Landing so I don't know the answer to your questions.
But if you make a back-up of your game, you could try it to find out. Just don't save. And when you do save, save under a different game so your original save stays intact. Or restore your back-up when needed. The house you could save in the bin and even export/share to the Launcher. Only from the Launcher you don't upload to the Exchange but open the folder Export where the house has an .sims3pack after sharing. You could back-up exports as well. In case you reinstall the game, you can reinstall those exports in the Launcher so the house will be in your game again.
If you play with just the mom and son, if that's your household, I think you will keep the house when the mom passes because the game isn't over. You still have one member left from the household so I assume the son can stay in the house. If not, you can manipulate it and place the son in the house during EIG.
Hope this helps. :smiley:
EDIT: make back-ups anyways.
EDIT II: When you travel to the other versions, just don't do elaborate things when you travel there just to test if she retains her home. That seems important to you so just in case it turns out she can't retain her house, you don't have extensive gameplay in a game that you won't keep because if you do she loses the house (I hope you follow my logic here).