The court decided YES.
http://abclocal.go.com/kabc/story?section=news/local/los_angeles&id=8034597

This sort of thing drives me crazy. This woman made the ultimate sacrifice. Now her Ex wants to exclude her and her parents from their lives. Obviously, the children need a lawyer as well. We definitely have to stop measuring people by their physical assets and realize the spiritual beings we ultimately are.  If I had been the judge, I would have had to fine the husband for having the nerve to even bring this to court, mandated sensitivity and ethics courses for him and his side of the family, and thrown the case out of the court in the category "AYFKM!".  How this was even considered to be put in the system is quite disturbing.
I don't think our tax dollars and court resources should be wasted on such obviously outrageous behavior.  The lack of common decency of the husband to pursue this in court, makes me wonder if their mother should not counter-sue for total custody.

It is shocking to me that this even ended up as a court case.  I can not even imagine the dysfunction in the marriage, but it should never be played out using the children as pawns.  Of course their mother should see them!

In addition to Bernadette's update above, here is more from MSNBC:

Attorneys for both sides praised the tentative 10-page order issued by Superior Court Judge Frederick C. Shaller, who ruled after a two-week hearing that 34-year-old Abbie Dorn would be granted visits of three hours a day for five days each summer at the home in Myrtle Beach, S.C. where her parents care for her.

Lisa Helfland Meyer, attorney for Dorn's parents, said the decision set a precedent for "every single parent out there with any sort of disability."

"I think this is an astounding victory," Meyer said at a news conference. "The court held that this parent has the same right as any other parent to have visitation and a relationship with their child."

Shaller also ordered that the children could have a 30-minute monthly videoconference with their mother, a move Meyer said would establish a "wonderful continuity" between mother and children.

There's more, read it here.
 

i am a single disabled (quad ) father. i was in the middle of a custody battle when i was paralyzed. my mother was able to follow up my case so that my mother and ii sshare primary custody. granted the mother was already deemed un fiit to care for her son(in CO). that is hard to  believe the court would restrict visits based ssoley on a disability . iisnt that blatant discrimination? what else is the court basing it's ruling on?

Of course a person with quadriplegia should have the right to visit his/her children! What kind of a question is that? This seems to be a guaranteed human right (except maybe in cases where the parents are abusers of the children). I know people who do not agree, but I think they are using the fact that one parent is disabled as a way to take the kids away from the other one. Unfortunately, I am personally aware of such a situation. I pray that people will not try to hurt one another in custody battles. Look at how you would feel if the shoe was on the other foot. Would you want to not be able to see your children simply because of an accident?? Love knows no bounds!

My husband is a quadriplegic and has helped me raise our daughter.  She was 6 months old when he was injuried and is now 3 1/2.  Without his help, she would not be the child that she is today.  So obviously quadriplegics should have the right to visit kids.  Just because my husband cannot physically do things for our child does not mean he cannot parent.  I know lots of parents who CAN physically do things for their kids and don't nor do they parent.  Your physical disability does not dictate your parenting skills.  And because of the wonderful father that my husband is, he was voted Dad of the year this year.  Our daughter loves him to pieces and actually listens to him more when it's just the two of them.  She has learned that although her dad cannot move, he can tell her what she can and cannot do since he is still her father. 

Thankfully the courts ruled correctly this time since those kids need their mother.  They need to see how strong and brave she is to live with that disability and to fight for her kids.  It also shows her kids the love that she has for them which will teach them more in the long run than what their dad taught them by bringing that case against their mom.