It is likely that with these facts the father can get an order for custody. You should present this matter to the judge after consulting with an attorney to fully discuss your case.
Drug rehab or not doesn't dictate an answer to your question. If parents can't agree, a judge will decide where the child lives based on a decision as to what is in the child's best interests. There are no fixed or simple rules, but where parents live in different countries the most likely result would be to continue the status quo.
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