Legal Question in Family Law in Alaska

It depends on what the judge thinks.

You mean VISITATION, because you are asking about a NON-CUSTODIAL parent.

Is the allegation that the children might be infected, or that the fact that the parent contracted the disease somehow is evidence of sexual promiscuity which in turn might somehow be harmful to the children?

I don't believe that, absent something you aren't telling me, there is any real danger of the children becoming infected. However this should probably be supported by expert medical testimony. And the suggestion that this might harm the children in some other way likewise doesn't seem very convincing.

Therefore, in all likelihood, the answer is no. Having this disease is not a good reason to deny visitation.