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First time mums

My husband has an alcohol problem, am I wrong?

My husband and I have a 3 month old child together. He has been acting strange ever since he was born... slurring his words every other night and acting drunk. It has affected him caring for our child. He has bumped his head while trying to put him in the cot because he doesn't see the length of the cot properly and has put him to sleep with a dirty nappy and without any pijammas on... just naked in a dirty nappy in the sleep sack. I've told him when he gets like this that he needs to sleep in the spare room as I don't trust him with our child... I was so scared something was wrong. I thought maybe dehydration, brain problems/tumer, sleep deprivation. He went to the doctor and the doctor said he is low in b12 and iron but that's it, everything else seems fine. He has been okay for the past 2 weeks then all of a sudden I catch him (4th time since I was pregnant) hiding in the garage, drinking a bottle of red wine (I didn't even know we had any). He pretended he was looking for something for dinner, he wouldn't let me pass. I passed and saw half a bottle of red wine. He said he didn't drink any, then said he did, then said he put it in our dinner (butter sauce pasta... the sauce wasn't red at all!). Lately I haven't been having any drinks when the baby is asleep (I used to have a half glass to unwind) because he is now co sleeping mid through the night and it's not safe if you have a drink.. so I don't. He has admitted that he can't just have 1 glass like I can. He has the urge to finish a bottle. He says he wasn't drinking all the other times when his words were slurring, but I can't help think he was but I just didn't catch him those times???
My only family live interstate (15 hour drive). I could stop along the way. I am thinking to head there tomorrow... but can I? Will I get into trouble taking our child interstate? I just have no one here and I worry that his alcohol will impact our child!! I feel he needs a wake up call... please be nice as I'm do stressed and don't know what to do. But I'd love some advice