My cousin's widow flipped out when she found out my aunt and uncle put their entire estate in a trust for their biological grandchildren?

The aunt and uncle are well within their rights to bequeath their estate to whoever they like and the cousin's widow's child has absolutely no legal standing to it. She seems pretty crazy which appears to be the aunt and uncle's motivation to exclude her and her child. She is not in line to inherit anything even if she could prove mental illness and an attorney will presumably tell her that when/if she consults one.

You need to have YOUR legal advisor nip this in the bud before she starts spending money on lawyers, which could eat into the trust fund that you administer.  Just letting her stew on it isn't healthy for anyone.  Get it cleared up by having someone explain the facts of life to her: it's not her place to decide "what's fair" for how anyone else gifts their money to others.

Let her challenge it in court, there is nothing to challenge.  They are free to do whatever they want with their money.  She has no chance whatsoever of being successful.

It's not just that you should defend the trust as written. It's that you HAVE to defend it, because the grandchildren can come after you if you don't. They have an excellent claim to the funds, eventually.

Aunt and uncle could be "unfair" in life, and they can be "unfair" in the trust. The courts will enforce their wishes as written the trust. The chances that they were actually so mentally ill, that the trust will be overturned ... those chances are practically zero.

The only (slim) chance that she might have is that the adopted child was not named in the will / trust; in that case the law presumes that the child was accidentally "forgotten".  But even then, it's your duty to defend the trust unless and until a court reforms it.

If it was a legally prepared Will it will stand up in Court.  Any properly and legally prepared document that meets the requirements of the law will stand up in Court.

Legally, there's nothing to be done.  What the will says is what it says.

But, I can understand how she feels.  She looks at all the kids as being equal.  To give some kids money and some kids no money is very unfair.  But there's nothing that can be done about it.

Essentially none, but if she files a claim, it is your legal obligation to protect the trust and the estate. You must hire a lawyer if a claim is filed. You are correct in your position, not only nothing you can do, but that you are going to protect the wishes of the deceased. The cost initially for your lawyer can be paid by the funds. You should seek attorney costs in your pleading because the case without any proof appears frivolous. If the child was specifically excluded that is even better than not mentioned at all, but your case looks solid. 

About 0 and any lawyer she talks to will tell her the same.  But, they may threaten and all that BS in hopes you give in. It will save you the cost of a court battle and all that jazz. As far as insurance money she received for the death of her spouse, that does not play into anything in any manner and should not be brought up in these discussions.

It costs many thousands to challenge a Will in legal costs, so it is very likely she is blowing hot air anyway once she realises that she will need to pay and if you a executor need to depend in court WHEN she loses she will have to pay the estates legal costs as well

She might delay things, but I doubt she can do much more than that.