R.,
It would benefit you to speak to an attorney who is in your county, and visit the law library in your county.
What I would recommend is getting a plan of action in place, for the just in case something happens, that way you are ready for anything.
First, set up several stipulations or "hoops" for this woman to jump through (drug free, random drug tests, proving that they attend parenting classes, clean record (no DUI's /Arrests, etc), and several counseling sessions and other family counseling intervention type things before she has access/visitation to the child.
If she is she's serious about being a positive role model in this child's life, she should not be upset by trying to prove herself to your family, the courts, and any other series of people set in place to determined if she's fit or not.
After which, I would request a that she is introduced gradually to your grandchild, in a supervised setting (your home)for let's say 30 minutes a week for 3 months, then an hour a week for the next 3 months. Moving up for a full year. This is also to benefit the baby, and also to see if she will follow through with this or not.
If she misses more than let's say 2 "sessions" she is docked her visitation rights and you start over again, or she does not progress forward and get to continue on with the plan.
Most people who throw fits like this, just want to be heard, but they are not determined and not willing to put for the effort required to be apart of the child's life.
I am not sure what a lawyer will agree to, but if you go in with a game plan of being willing to cooperate a judge usually likes this and it shows that you are willing to work with the other party and yet if it somehow becomes no longer in the best interest of the child, the visitation is terminated.
You can always insist that there is no sleepovers, and there is no leaving the property, or whatever, until let's say the child is of let's say X years old or something like that.
I know with an infant, you can say, "the baby is breastfed" and it would keep the baby with its mama longer.
I would just start lining up your ducks, just in case this woman happens to get the right lawyer and the right ear of the right judge to make her case heard.
Good luck to your family and to your grandson.