The German word for mother would make a fun choice for the 2 moms.
They say Mutti(moo tea).

Or how about the Ferengi(Star Trek) term Mugi(moo gee).

Just some thoughts.

I also agree that, if you are lucky, your child will likely make his or her own choice.

I have the privilege of being a stepparent. When my wife and I married, the boys were old enough to make their own decision about how to call me. At one specific point just prior to our wedding, I did explicitly give the boys the permission to make their own choices — till then I had been "Glenn." Ultimately, they never really settled on just one choice. I asked permission to refer to them as my sons, which I still do, unless context demands greater clarity.

Over the years, I’ve enjoyed a rich experience of nuance, from their calling me Glenn (with tenderness ranging to both extremes), through the collective “my parents,” to the traditional “dad.”

Now that the boys have their own children, the nuance continues. When the oldest grandson was born, I certainly did not want to usurp the grandfather position from the boys' biological father. I was unsure what our son and his wife would choose. As it turns out, they were heading for “grandpa.” But, while my grandson was still in the babbling stage, I was tending him in the next room, and making a joke by loudly coaching him to say “grandpa” as his first word.

He popped out with something sounding like “oom-pa” and I jokingly declared victory that his first word was “grandpa.”

Now, as a five-year-old, while “grandpa” occasionally slips out, “oompa” is my primary label to all — him, his younger brother, and younger cousin. I think it is a keeper.