I’m so sorry CTLAWYER for you and MRS. CTLAWYER’s loss… Thank you for asking for our humble opinions on this majorly important matter.
Here are my thoughts:
Answer #1: Yiddish name; it’s personal to your wife’s mom. Using her Yiddish name, the name that comes to mind and heart when your wife thinks of the name that speaks of her mom’s neshama, honors their maternal bond. It’s authentic.
Answer #2: One-hundred percent, inscribe both stones, but personalize the one near husband #1 in a way that both respects their marriage together, all the while making it clear that she had since moved on to another marriage, and thus isn’t buried beside husband #1.
B’Hatzlacha, and may whatever you choose to do be good and bring good, enhancing your mother-in-law’s memory as a blessing in this world and the world to come.