I'm not going to really profess my opinion on this, or talk about private information, but there are certain facts that can be looked up that I did want to point out to clarify things.
The current "Gygax Trust" was not established upon Gary's death, nor was it apparently an inheritance trust.
Since the founding of Trigee Enterprises, all of Gary's intellectual property was owned by Gail Gygax, NOT by Gary Gygax--Gary was "under contract" to Trigee Enterprises--and about 95% of Gary's output was done as Trigee. It was an arrangement Gary and Gail agreed upon for various reasons. So, basically since 1986 or so, all the stuff Gary worked on post TSR was owned by Gail, not Gary. In short, as far as I know, Gary couldn't even choose to leave any IP assets to his kids unless Gail agreed to it. In this response, I'm going by what I knew of Trigee from Gary himself, and my years working for him, along with things others have learned--there could be some details in the incorporation docs or elsewhere that might clarify things, so I won't say this with 100% certainty.
Trigee Enterprises was I believe then converted into or owned by the Gail C. Gygax Revocable Trust. Note that this is not a family trust, and she is listed as the sole recipient of it--I believe this trust was established years after Gary's passing. Documentation on this can be found at the Trademark Board for the active Gygax trademarks -- all documents say "The Trustees of the GAIL C. GYGAX REVOCABLE TRUST, a Wisconsin trust, the trustees comprising of Gail C. Gygax, a United States Citizen". So the current trust is, as far as I can tell, not something any of the kids are involved in, nor anything that was established as the estate when passing. (Could be wrong but I doubt the Trademark board would word it like that if there were other trustees involved).
In terms of the court, I don't believe Gail ever took her will to probate court. That's probably why there's a dispute now.
Thank you for this. Very informative.