Am I too hasty?

Me personally I would find calling him without the best friend on the line a red flag. Emotional affairs can start from friendships . Not to put that idea into your head but it is a boundary that shouldn’t be pushed. I to am strugglying in my realtionship. If he can’t respect your values and boundries how can he respect u with a child? Drinking definitely has become normalized in society. But alcoholism is a deep issue . I got sober for my kid. / lot of men don’t even when the woman does , but drinking is def an issue and I do not think your over reacting for caring . He should be limiting people and things that could tempt him to drink more . If he doesn’t seem to think it’s an issue Thats the problem to begin with . The only way to grow and change is to first acknowledge u have a problem. Not taking accountability and blowing up on u in a way is unhealthy and not fair . I think u deserve better . No relationship is too far gone to fix . But Thats only if both parties are willing .

Personally, I wouldn't have any concerns about the calls- unless there were other red flags with the other wife. I have a bunch of male friends and my husband has a bunch of female friends- all purely platonic. I actually find it a bit of a red flag when men don't have platonic female friendships.
The other issues definitely need work. Have you had a sit down talk with him about your feelings around the drinking and the job hunting? Is he willing to hear you out and make changes?
If he is then that's great and I would wait to see if he actually does implement those changes. But if he's not, then you need to do what is best for you and your baby.