Support is not tied to visitation/custody (other than depending upon the share of physical custody), so you would not have any concerns there.
Most courts in VA that I have been in (between 10-15 different jurisdictions) grant joint legal custody. There have to be very extreme circumstances for the court to deny joint legal. That has to do with major life decisions regarding the child - such as medical care, education, and the like.
You already have sole physical custody. What you don't have is an order in place setting the custody and visitation schedule. However, if your husband does not exercise visitation, then the courts likely will not do much about it.
Since you are separated, you could simply formalize custody/visitation within the final decree of divorce or within a PSA that is incorporated into your divorce decree. Setting a schedule could well make your life easier and may encourage your husband to follow the agreement.
Please note that this response is based upon the limited information available in the question. In addition, it is not intended to create an attorney/client relationship and is offered only as general information and not as legal advice.
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