This answer is No.. If you buy a new home and default on it then you will lose that home by way of foreclosure..
Your lender may inquiry about the first home but this is standard. It does not mean they will go after your moms home.
Just for you to know, you can homestead the new property and your mom can still homestead her home.
So, make sure you homestead the new home as this will be your primary residence.
I don't agree that the second home would be investment property...under the IRS rules you are allowed two residences...if you own the first house, free and clear, then the mortgage office might explain what you will need to buy house #2...but it will not be investment property...