I have gone to court and had my infant daughter legitimized. She is 8 months. I found out she was my daughter through DNA testing when she was 6 months, since then I have been fighting for custody. At our first court hearing the judge agreed to the mothers offer of visitation, 2 days a week for one hour and every other Sunday for 3 hours. He told us to work out the details verbally and in the meantime he ordered a guardian ad litem. I am still waiting to hear from the GAL, but now the mother refuses to allow me to see my daughter. Even though I pay her weekly child support.(which has not yet been ordered, I am just doing so because it is the right thing to do). At this point, I have no court orders. I am at the mercy of the law that is made to protect children from dead beat dads. Can she do this? And if so, how bad will it look to the GAL and the judge?

So, when the judge ok'd the mother's offer of the visitation arrangement you mentioned, he didn't order it? Either way you need to go back to court - either to get a visitation order or to hold her in contempt for not being willing to work out the arrangements for the exact schedule if it was ordered that you both do so by the judge.

Once you have a court order, the police can enforce it if she fails to adhere to it.

He did not order it. At the time she was 'allowing' me to see her on occasion. I always wanted more time but she has been difficult to work with. After court, she became very angry as she now knows I am trying to prove she is not the great mom she claims to be. She can't hold a steady job. She lives with her parents and is almost 40. She has a drug and criminal history. The only thing the judge ordered was the GAL and our court system is very backed up... I'm just discouraged. I miss my daughter.

I live in Illinois, my other two children are both grown and in college. I was A very involved father and they are both willing to testify on my behalf

You need to separate some of this stuff. First the fact that you are paying support has nothing to do with the custody and visitation. Second, your fight for custody is also somewhat separate from your visitation. You need to deal with these issues as separate items.

So you go back to the judge, and you ask that he issue an order for the visitation that the mother agreed to (as you said). You don't say anything about support or custody at this juncture. You simply say that the mother agreed to 2 weekdays and Sundays but now refuses to allow it. Ask the judge to hold her in contempt or to make it an order so she has to comply.

I understand that these are separate issues legally. I mention them because I think it speaks volumes of the character and intentions of both of us. I will let you draw your own conclusion...
I hope that the legal system has discerning eyes as well

Yes, I understand, but its not us you need to convince. Since this was a question about law asked in a law forum, our responses will deal with the legal issues.

I find it reprehensible when parents use children as pawns in their battles between themselves.

When you are arguing for custody, you (or your attorney), can point to her reneging on the visitation offer to illustrate character. But getting the visitation enforced is a simple matter of presenting to the court that she offered this schedule, that the court approved it, but that she immediately reneged on it.