Divorcing (talaaq) three times based on a belief that it is obligatory

Me and my wife have had a rough couple of years. We got divorced when we both had little knowledge of this religion. For the first time she is willing to work out are marriage and I thank Allah that she has been thinking about this. It is imperative that this question be answered for me because it involves a family being united or seperated. When we first got seperated someone told her that you have to give talaq 3 times, so i gave her the first talaq willingly from my heart. After that we tried to work it out, But someone told her that it is obligatory to give the 2nd talaq even if one does not want to after 3 months and a 3rd one is obligatory after 6th months. So I was angry and didnt bother researching and asking about this. So when the 3 months were over i gave the second talaq without really wanting to but i thought i had to. When the 6 month came, i thought it was a sin upon me if i did not give it to her because this is what a view ignorant people told her and myself. So i waited longer then the 6 months sad that i was forced to give her the last one knowing she will not be available to me unless she marries, so out of anger and sadness i gave her the third talaq because i was told it was obligatory on me to do so. After that we were apart for a year since then but i always wanted to work it out. When i started studying fiqh under shayukh and in the masjid they told me to relate to them how i did my talaq. I told 3 or 4 people and they said subhanallah you may still be married if you thought you had to give the third. So now i relate my question to a proper scholar. We both now want to work it out, but this one last steps in the way. We live far apart now and I havent seen my son in 2 years because of no travel money and the only way to see him is to live with her and him again. So I wanted to know if she is still lawful for me because we both want to work it out. No shaykh has answered my question and i need an answer quickly, and i fear i may follow my desires if i do not get a response because i havent found any answer related to my situation.