Transferring Home Ownership
A: First I want to tell you how much I love that you're living with your grandmother. You are giving your children an incredibly rich experience all the money in the world could never buy.
I don't want Grandma to give you the house right now. Tax-wise, it's far better to inherit it. (To ensure that the house goes to you as intended, she needs a revocable trust with an incapacity clause naming you as the successor trustee.)
When you're gifted property, you take on the giftor's cost basis—what someone paid for an asset. In terms of a home, it also includes any upgrades. The IRS cares about your cost basis because the difference between that and what you sell something for (minus any exemptions) is taxable. Let's say your grandma bought her house ages ago for $25,000. Assuming she made no improvements, her cost basis would be $25,000. If she gives you the home now and you then sell it for $625,000, you'll pay a huge amount in taxes. But if you inherit it, your cost basis would be its value at that time. So if the property is valued at $625,000 when Grandma dies and that's when you sell it, you would not have any tax liability.
Moving isn't the answer. There's great comfort for older people in remaining in familiar surroundings, so I'd recommend staying put and adding on.