Can my husband be forced to take a drug test by the courts for a custody investigation?

I am currently remarried to my second husband. We have discovered that my first husband (and father of my children) has been neglecting and abusing my children. He has not been arrested, because there isn't enough evidence. However, I have temporary custody and he is only permitted to have supervised visitation. We are in a custody battle and he has accused my current husband of drug use. My husband did have issues when he was younger, but has worked hard to put those behind him. Can he be forced to take a drug test? How important is his background? My first husband's crimes were crimes against children, which is why I believe his background is relevant. His latest physical arrest was in 2011, and has outstanding warrants in 2 states. My current husband has not had any incidences or arrests in over 6 years, and none of them involved children.