You'll definitely want to consult with a trusted, local attorney. If helpful, even though it only pertains to residents in nearby New Hampshire, please see this link below for tips on how to secure sole custody (and challenges to doing so).
If there is a custody order in place, then you have to make a motion for modification based on the change in circumstances (father moving away). In that motion you ask for an order granting you sole custody. Another option would be to have joint legal custody (decision making), but that you would have residential custody. You also must make a motion for child support, since he is living with you full time.
For relocation, the father has to make a motion and he has the burden of proof to show that relocating the child is in the child's best interest. There is a risk that the judge would permit relocation, but it depends on the living situation of the child. You should consult an attorney who can give you specific advice based on your circumstances.
Child custody cases are generally very heavily fact-based because the general rule is determining what is in the child's best interest. In undergoing this analysis the court considers multiple factors, examining a multitude of facts. You should consult an attorney in your jurisdiction about the facts of your particular case to determine your best legal options with regard to child custody.
This is not legal advice. This response is provided for general information only, as a public service. It is not to be relied upon as legal advice and does not create an attorney/client relationship; nor is it an attempt to create an attorney/client relationship. Consult with local counsel in your jurisdiction about the specifics of your case, which is the only way to gain true meaningful legal guidance and/or representation.