Dead Beat Parents

Why is it that even if a parent is not paying child support they still have a right to see the children? To me if they can not come up with the money to support their kids all the time then they can not come up with the money for them to come and visit.
I have two children that live with me now. When they did not live with me I tried to make arrangements to send support their mother would not set up a bank account so i could send her a direct deposit every month. To top it all off she moved around a lot so i never had an address fro her and the kids. I was in the army at the time and during this I was going out for weeks on end training for a upcoming deployment. I was harassed at work about not paying child support. I informed them that i had no idea where my kids were to send support. I did everything I could to support them. The Child Support Enforcement agency that was coming after me ended up taking 50% of my paycheck every two week leaving me with barley enough money to live on. I ended up losing my apartment and became homeless (While active duty Army). I was thankful to have some friends that would let me stay with them.
Now the kids live with me full time, their mother does not pay and has never tried to pay child support yet she gets everything she asks for in court. I find this very unnerving, why well when I was paying out over $700 a month she took the children and moved out of the state and no one would inform me where she took my kids. They told me to my face that I had no right to know where she was living. It did not matter that she was hiding my children from me. She broke the law by obtaining Medicaid for the kids when they had free medical care threw Tricare (Military health care). They said so what she did nothing wrong, yet i got stuck with the bill to the tune of $10,000 +. Now they live with me and she does not work and stopped working when she got papers to show up in court for a custody hearing. A hearing that she did not even show up for.
The court left the visitation wide open allowing her to do what ever she wanted and left me with no recourse. She told me to Fuck off and if I wanted the kids I had to come and get them. It cost me the price of 4 plane tickets last minute. Still nothing was done to help me. Then I went back to court to get visitation set and she still got what she wanted. They didn't even care what i had to say. I was fighting an uphill battle with no lawyer which she some how had the money for. She still has not paid a dime in child support for over 4 years. I am told that the back support that should be mine I can not get because of some stupid reason.
Why is it that women can get away with so much yet, I make every effort to do the right thing and the same people try to throw me in jail. They make me feel like Because I have a penis and testicles I am the EVIL bastard no matter what. My daughter needed glasses it took my new wife and me two days to figure out that she needed glass yet, for size years my ex-wife could not figure out that my daughter needed glasses. My daughter has allergies to smoke, weeds, and pollen. My ex-wife still smokes in the house with her there and, there is not a damn thing I can do about it.
I feel that if you do not have money to support your ids then you should have no rights to demand anything if your mother or father. You should not be able to see them either. It might be hard on the kids for the time being, but in the long run it will be much better for them.