The provision to postpone the capital gains on the sale of a home by buying a new home was removed in 1997, and even then, it only applied to your main residence. It appears that you handle the situation correctly. You paid capital gains tax on the sale of House 1 when it was sold, and you paid capital gains tax on your half of the capital gain from house 2 when it was sold. Because House 3 was not owned by you, you are not responsible for any part of the capital gains tax on the sale of house 3.
The $75,000 could be treated as a gift or loan. If it was a gift, then you would be responsible for filing a gift tax return to report the gift in the year it occurred, although gift tax is not actually owed unless your lifetime total of all gifts is more than $11 million. Likewise, your mother has just given you a gift of $75,000, and your mother would be required to file a gift tax return.
If the $75,000 is treated as a loan, the IRS requires you to report interest income on that loan, and if you don’t charge interest, you must report interest income that you would have received if you charged interest at a market rate. This is called imputed interest. For the past several years, the appropriate market rate has been 2% or less but it is recently gone up. It is a variable rate and can be calculated on a monthly, semiannual, or annual basis depending on what is appropriate for the type of loan. You are required to pay tax on imputed interest because the IRS position is that if you are going to make a loan, you must conduct your business in a businesslike manner and that includes charging interest, even to a family member.
I don’t see any real harm in treating this as a gift that you made it to your mother several years ago and that your mother has made a gift to you now. However, the gift tax returns would be required to be filed. It would certainly not hurt to have a professional review all of this, because some of the things you describe were not in quite the right language, so I am not 100% confident that I understand the situation and the ramifications.
