MIL added our name to the the grant deed prior to her death. When we sell the house, what is the cost basis of the property? The original acquisition cost of the property? or the FMV of the property when our names where added to the grant deed?
You are going to need a lawyer, or lawyers, to sort out who owned what when, and how much of the property was a gift versus an inheritance. There might also be a question about whether your mother-in-law retained a life estate when she put your names on the deed. A life estate could be specified in the deed, or it could be implied or de facto. The lawyer(s) will have to examine the exact wording of the deed and any other related documents, as well as your mother-in-law's will and any probate documents. There are issues involving real estate, wills and estates, and income tax, so you might need more than one lawyer, or a law firm that has lawyers with expertise in all three areas. If you know the lawyer who prepared the modified deed, that might be a good place to start.
The usual rule, for a gift, is that the recipient's basis is the giver's basis (what you mother paid for it). But there is an exception for the gift of her home, where she retained the right to live there ("life estate"). If she give away an asset and keep a life estate in that asset..... the cost basis of the house is "stepped-up" to the value of the house on date of death (IRC 2036)
To expand a bit on what I said in the first sentence of my earlier reply, it's not clear how much of the house was a gift and how much was inherited. You said that your mother-in-law added your names to the deed. You didn't say that she removed her own name. If she added your names but did not remove herself from the deed, then she remained a part owner, and she only gifted you a partial interest. In that case, one of the things you need a lawyer to sort out is what each owner's share was. The possibility of a life estate, which makes the gift incomplete, adds another level of complication.
If your mother-in-law was still a part owner of the property at the time of her passing, then someone inherited her share. That is not determined by the deed. It's determined by her will, or by state law if she had no will. And the basis of an inherited share of ownership is different from the basis of a gifted share.
If she did remove herself as an owner and deeded the entire property to you, you still have to deal with the life estate question. And since you say "we," "us," and "names," it's clear that there are multiple owners involved. An examination of the relevant documents is needed to determine what each owner's share is.