You need to sit down with a local tax professional and go over all the details of the various transactions. (At least for houses #2 and #3. House #1 is pretty much water under the bridge at this point.)
Here are a few points for you to be aware of, but don't try to clear up any confusion here. You can discuss these points with the tax professional.
When you sell a house you can do whatever you want with the money that you get. But the tax is based only on the details of the sale. Putting the money into a new house does not affect the tax on the sale. (There used to be a rule that you could defer, not eliminate, the tax on the gain from selling your principal home if you used the money to buy a new home. But that option was removed from the tax law about 25 years ago. In any case, it does not appear that you sold your own principal home at any point.)
It's not clear where the $75,000 came from if the proceeds from house #2 were split between you and your mother. It's also not clear whether it was really a loan. If it was, there are additional tax considerations.
A QCD has nothing to do with a deed. A QCD is a Qualified Charitable Distribution, a distribution to a charity from an IRA. So it's not clear what you did with the deed.
A home that you own, partially or entirely, that a family member lives in is not an investment property.
