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Hello,Thank you for allowing us to assist you with this problem. I am not fully aware of what prior steps you have taken.
Yes you are correct there was no mandatory need to have one parent listed as domicilary so long as the parents can agree on all terms concerning the child. However, it may be hard to "make the attorney legally responsible" unless your son or his ex-wife suffered a real harm from the advise. The solution is to create a modification of the current custody agreement removing the title of a domiliary parent. If there was a harm suffered due to the incorrect advise then you must be able to convince a court that it was an definative statement by the attorney and not just a strong suggestion. There are benefits to having a designated parent as domiciliary and because of those benefits that is why you would have to convince a court that it was more than just a suggestion.
The two parents can create a new agreement in writting signed by both parties referencing the change to the prior agreement. I realize given the bad experience you had with the prior attorney that you may wish to do it yourself but you really should have an attorney prepare the document for you.