What do I need to do when going about getting visitation right and what's an estimate for a case like this cost?

Besides the fact that prohibits attorneys from posting their fees as an answer, many factors affect the fees, including whether or not you ever legitimated the child, the county the mother lives in, details of what has happened to date, and how cooperative or uncooperative the mother is during the court process. In some cases you having a live-in lover could hurt you with some judges, so you may end up with advice as to changing that status either by marriage or a change in living arrangements. Custody battles can become very expensive but some are resolved for far less than others. Your first step is to sit down with a lawyer, share the details and discuss the pathway to proceed.

You should first try to work it out with mom before going to court-it's in everyone's best interest to try to agree without court intervention. If y'all can agree then you need to file an agreement to solidify visitation, child support, etc. But, if she's not willing to cooperate for the best interest of your child then court filings might be necessary. Seek legal advice to help you try to work it out amicably but also to protect your rights and relationship w your daughter should mom not cooperate.

What does the custody/visitation order say? Generally, it may have detailed visitation plan, open-ended order allowing the parents to work out visitation schedule between the parents, supervised visitation, or no visitation at all. If you believe that visitation court order was violated, you can seek legal assistance. Your attorney can send a letter notifying the other parent about legal penalties for not obeying the court order. You can also file a Motion with the Court for contempt of court. You can request attorney’s fees and other costs with this motion.

If you do not currently have a custody and/or visitation order providing you with a form of custody and/or visitation, you must seek that through the court. Since you and the mother were not married when you had your child, you will have to file a Petition for Legitimation. In a Petition for Legitimation you will ask that the child be legitimized and you can also seek custody & visitation as part of the Petition. The cost of this will vary because there is a filing fee for the Petition for Legitimation and the filing fee varies depending on the county in which you file. The filing fee is the fee you pay to the clerk in the county in which you file. There will likely be a service fee because you will need to serve the mother by the sherriff's department in whatever county she lives in at this time or the county she works in if you choose to have her served at her place of employment. If you choose to hire an attorney to represent you they will also have to prepare for your hearing on your Petition, and if the mother does not appear, there may be more than one hearing.

I am assuming that all you have established here is paternity and an order for child support and that you have not legitimated the child. If the child was born in Georgia, and the child was born out of wedlock, all legal rights are vested with the natural mother of the child. You must petition the court to legitimate the child, establish some form of custody, parenting time (visitation) and perhaps even re-address child support. If you have legitimated the child and there is currently an order incorporating specific provisions about parenting time AND you can show that the mother has refused to allow you to have time with the child without good reason, then you may have a case for contempt. Costs for these cases is very fact specific and depends on the nature of the case and the people involved. Call some family law attorneys in your area and set up some meetings for pricing and more information.