do i give my husband sole custudy

As a preliminary matter, it is important to note that there are legal distinctions difference between custody, guardianship, and adoption. Each of the aforementioned terms has different legal standards that must be followed before a court makes a decision.  When your husband uses the term guardianship, what is his intent? Is it his goal to give "legal custody" to a step-parent?  If so, does the stepparent have a relationship with the child? If he has not remarried, is this statement made in the abstract and there is no new wife? When it comes to matters of custody, the court's primary concern in the best interest of the child, as defined in Virginia Code Section 20-124.3 What is best for a child will be governed by the facts in a particular case as applied to the applicable law. In the same question, you appear to be asking about an adoption? It is not clear to me what you are asking.   If you are the biological parent of the child(ren) in question, and your rights have not been terminated by a court of competent jurisdiction, you have a right in the care and custody of your children.  If you are fearful that your husband will try to permanently divest you of the care and custody of your child, perhaps, you need to consult with an experienced family lawyer in your area to discuss the legal implication of any decision you are considering, as it relates to your legal rights.  Unfortunately, your question as presented cannot be answered in this forum.  Lawyers.com offers general information and not legal advice. In order to obtain legal advice, you need to meet with an experienced family lawyer in your area to discuss this matter in greater details.  Most lawyers charge for an initial consultation, which is often based on a lawyers hourly rate.  I suggest that you discuss these practical matters before making an appointment to avoid any misunderstandings or confusion. Best of luck~