When her mother passed she left a will that left everything to her granddaughter.
I assume this granddaughter is not your wife's daughter.
the litigation between myself and the wife's sister and granddaughter has resulted in a stipulation entered into in a different court. The stipulation had a clause stating "granddaughter waives any and all claims to the following properties: (i) wife prop 1 (ii) wife prop 2."
That's not really clear. For starters, is the granddaughter an adult or a minor? If she's an adult, why was your wife's sister involved at all?
Unless there are facts you haven't told us, the granddaughter waiving "any and all claims to the . . . properties" is meaningless because the granddaughter never had any valid claims to the properties. RATHER, the properties are owned by your wife's estate. Your wife's mother's estate is a beneficiary of your wife's estate, and the granddaughter is a beneficiary of your wife's mother's estate.
With that said, did the granddaughter only waive claims to the properties? Did she also waive any claim against your wife's estate? Even more importantly, has the personal representative of your wife's mother's estate (I'm assuming the error in appointing you was eventually rectified) waived the mother's estate's right to receive proceeds from your wife's estate?
Now, I am trying to sell the two properties of my wife's estate. Since both my wife's mother and I should receive shares of these properties under Massachusetts law, how do I proceed given that granddaughter waived her rights to the properties?
Here's the most important question I will ask in this response: What does your attorney say? If your answer to that question is that you don't have one, then you need to retain one because your question is not one for which you should be relying on anonymous strangers on the internet. With that said, the answer to your question depends to some degree on how you answer the several questions I asked above. However, if you are the court-appointed PR of your wife's estate, you should have the authority to liquidate estate assets.