My mother had assets in her name alone, in her will she gave it to her children.
Now, after she has passed, her husband (my father) is claiming this is his money.
Does the husband have a claim on money in his wife's name?

In many states a spouse cannot completely disinherit another spouse. This could invalidate the will. If the will is held valid, then the money is the children's

If there is no will,
If the money is in a joint account, it will depend on how the account is named, possible in joint accounts it would be his.

But in general if the will does not go along state law, the husband could object in probate court and ask for the judge to give the money out according to state law.

I know in one state I lived, I could not write my wife at completely, if I did, she could have overturned the will and gotten 1/3 I believe.

So the kids need to hire a good probate attorney