I have a daughter who at the moment is in a mental ward of a hospital.
Her husband recently served her divorce papers, at the hospital.
She is in no way capable of going to court at this time. Can they do this?

Can they serve her with papers? Yes

She can go thro a psychological evaluation to see if she's fit to stand trial.

In all the pre-motions and stuff, she doesn't have to be there, her lawyer can do that.

If she is not competent, and has a guardian assigned, they can serve the guardian.

I will ask this, are there children involved ?

A lot of property ?

If there is little property and no children and he wants a divorce, then one merely has to sign the divorce papers that are draw up. Many men and women who have no children or that can agree merely hire the same attorney and just get divorced

She does not have a guardian at this time, but I am in the process of getting her a temporary guardianship. There is one child, 3 months old. At this moment she is not competent to have custody, but I want to make sure that she will still have some rights after she is back on her medications.

She will always have rights, but often will have to prove she is mentally sound to be capable.

Next does the father even want the child ? Sadly many don't.

But believe me no child custody case is ever over. Till that child is 18 both parties can ( and often do) go back to court every year or even every few months to have this motion over turned to have this motion heard.

When my two oldest ( now 30 and 28) were young we changed custody 4 times before they finally turned 15 and decided to move and live with me.
She got first custody, I went back when they were about 6 and got temp custody, she got them back, I got them back about two years latter, she came back and got them and finally they wanted to come and live with me.

Believe me the cases are hard. I had evidence in every case where their money abused them physcially, where she drank, brought various (dozens) of men home, would leave the children at home by their self for hours ( latter with younger children from other men)

I always had a higher paying position, large home and so on. But as you see twice even with that evidence I still lost custody. So in a couple years I would refile. Depended at times on the judge I got and other issues.

Most likely at this time, what I would push ( hire an attorney to work on your daughters behalf) pospone the divorce proceedings pending the health of your daughter, OK if the man gets temp custody, since he most likely already has them physcially. Get grandpartent visitation right for now, so you can keep in contact and not let them get poisoned about their mom.
Demand a complete accounting of all assets as of now, so that he can't hide them prior to division of assets. Lotsof other things I am thinking of, but hiring her an attorney would take care of it,