Toddler will NOT sleep but dad is against melatonin. What should I do

Idk what to do. I need opinions or advice. My son is 3 and I’m dead serious when I say he does NOT sleep at night. I’m talking he stays up until 4, 5, 6, 7, in the morning EVERY. SINGLE. NIGHT. I’ve never in my life seen a kid go without sleep the way he does. This has been going on since a little after he turned 2. It’s so bad that I finally made an appointment with his pediatrician to talk to them about it and basically they just recommended to give him a small dose (.5mg) of melatonin at bed time a couple times a week and said if that didn’t help they will give a referral to have a sleep study done. However, I haven’t even gotten to see if it works or not because my bf/his dad is 110% against it and will not allow me to give him melatonin at all. He said he’s not gonna allow me to “drug our kid to sleep”. We’ve argued over it a lot but he says he don’t care he will never be okay with it. I have tried every thing under the sun to get him on a better schedule and get him to sleep at night. I have tried it ALL. He just won’t sleep at night. I personally would be okay with a small dose of melatonin a couple nights a week but his dad isn’t budging on his opinion towards it which I feel is unfair because his dad goes to bed every night he gets to sleep and I’m the one left up with our toddler all night long until daylight most nights. I’m really struggling because we also just had another baby who is 1 month old so I’m not only dealing with our toddler who’s up all night but also a crying newborn who is still adjusting. I’m just ready to lose my mind at this point. Ive even thought about getting melatonin and just giving it to our toddler anyways without his dad knowing but that would probably be messed up so I haven’t. He will NOT stay up at night to help with either of the kids so that’s also out of the question. What should I do.🫠