If there is sufficient proof to prove by a preponderance of the evidence that conducting such tests before each visit are in your child's best interests the Court may order that done. You would have to file a Petition with the Court making that request, meet the necessary burden of proof, and argue to the Court why its in your child best interests. If there is already an Order in place, you would have to modify it upon the showing of a material change of circumstances.
You can file a motion with the appropriate court asking for drug testing. The motion would have to thoroughly explain why you feel the testing is necessary. Further, you would have to explain why requiring the father to have testing done is in your child's best interest.
You can also seek supervised visitation if you feel the father will be a threat to the child's safety or feel that the child will not be comfortable if left alone with the father.
Legal Disclaimer: The response herein is not legal advice and does not create an attorney/client relationship. Mr. Whiteru advises the questioner to contact an attorney in his or her state and obtain more detailed counseling regarding their legal issue.