I have just read all this and caught up. It seems that this is moving forward with lawyers which hopefully means it will be resolved for both of you quickly so you can both get on with your lives.
It is good you seem to have support and you seem to recognise that the key issue and often battleground is the children. I do have some questions for you though. While the lawyers will sort out assets and divorce and custody will be decided by the judge, have you considered what causes a women to first file for divorce, presumably with children you are the bread winner, so what made her suddenly leave?. You described at the beginning you didnt see it coming and yet this some time later seems a drastic step. It seems to me while you are looking for support you havent addressed what it is your wife is going through. She has left with the children yet remained in contact so you can speak to the children. If she hasnt given you the address but the number and you have contact, then it seems odd to me that she appears to be protecting herself and the children for some reason, it is the only reason she would not give you the address surely, but is allowing you contact with both of yours children.
So while seeking support of others is a good, have you really addressed what it is that caused her to take such a drastic move. As a woman myself, and i know there are a lot of boys here, it is very unlikely a mother would remove herself from a family home, with both of yours children unless there was a major and significant problem.
Maybe there is some other support you need other than legal advice as it seems perhaps you have not addressed what has made her take such drastic steps. However she is still talking to you and contact with the children so it seems a future where you still have visitation and interaction with them is still quite likely. While it is a shock to the system to find the home empty where it was expected before i would stongly recommend before fighting a custody battle to seriously consider what it was that made her leave so dramatically and also quite honestly what it is that is really best for the children and this is where you may have to be seriosuly honest with yourself. From what you have said , and she is in contact then maybe you would be better not having a custody fight and it is more likely that a visitation plan and parenting plan can be worked out. This is more likely if you dont fight and show yourself to be understanding and to be honest pragmatic. While often fathers feel bereaved they have lost some access and control, in truth children need stability and a parent fight can go on for years , suck up a lot of lawyers fees unecessarily where often the woman just needs to be allowed to bring the children up and the father needs to support and in reality in most divorces the time you get is in reality not much less than you would if you were working and still together. It is just organised more.
Before you get all engaged with aggressive lawyers and into fight mode I would truly put yourself in the position of your children and ask honestly what is best for them and not what is best for you. They are not a posession or something to negoatiate over. Who honestly, if you the is such a big issue with your wife, is best placed to raise them. That often takes massive courage to make that step but before you fight for what you think is 'your' right, you seriously need to consider what is best for them. In all the cases I have seen , it is more likely she will overcome any hurts you have done to her if you give her custody and agree a good visitation schedule in a mature way.
It will settle everyone down so they can get on with their lives quickly and adjust rather than a long fight that will harm the children, if you are intent on fighting custody , remember that sole custody doesnt mean you dont get to see them. It is that part that needs to be agreed. And if she has moved but is quite willing to give you contact, my advice is ask her , using lawyers, to a visitation schedule, holidays , weekends etc, and make sure and this is important that you recognise she is allowed to have the same freedoms you are so always consider her time and needs and not just your own ie you get to be away from the children while you work. She will have a life to so make sure you factor that into any negoatiations. If you have done something wrong to her to make such a step I would address that too, admitting it is a good step and more likely for her to start to trust you and agree a more reasonable custody arrangement. it is certainly not wise to fight if there are still issues that she left for unresolved.
Often these get to come out in court, they get recorded, others end up being involved, friends, witnesses, freinds get turned as hostile witnesses etc and it can get very messy and expensive. So be clear before you go to court , what is it you are actually seeking, revenge she has left you, custody because you think tht is best for the kids or frightened because you dont think you will see them again. Clearly the latter isnt the case as she has already contacted you. I would think long and hard about the children before the 'fight'. You may get something from it, the lawyer will surely get some money and the children, hmm well they would certainly be the losers here. Sometimes iti is better to appeal for mercy than fight. From your words you seem intent on fighting, and that is never in the best interest of the children.