I'm surprised anyone thinks this is acceptable. Staying out all night when you've discussed it is one thing.
Calling at 2am and saying you're going to crash at a friend's house is one thing (although I'd still be pissed off if I we had three kids and this wasn't what was planned as it's massively irresponsible and putting all the pressure on you).
Letting your phone die at 2am and your wife having no clue where you are and staying out until gone 9am is just unacceptable.
If I were out at 2am and my phone died while my husband was at home with the kids (unlikely since I'd never go out til the early AM and leave him with the twins and vice versa) I'd firstly be using someone else's phone to get a message to them (yes, I have his number memorised but I'm sure someone he's with has your number is a fb friend or something) or I'd be going straight home so as not to cause unnecessary worry.
Before kids my husband went through a phase of going out, saying he'd be home by a certain time, hours after that point i'd get a phone call and he'd be off his face and acting like a total arsehole. I'd dread him going out. He was struggling with depression (life was pretty tough for both of us at this time). One night he was so pissed he ended up in a cab with someone random, dropped off miles away from home and somehow made it home despite the fact he could barely stand. I hadn't heard from him for hours by the time he turned up. He was nasty, over dramatic, falling around the flat, acting like a completely different person.
I absolutely lost my shit and told him I was done - it's just massively disrespectful to make your spouse worry like that, and to behave like a bloody teenager when you're a grown adult. He stopped drinking at that point for over a year. After that if he was going out he'd tell me when he'd be home and would actually be home by then, and not wasted. Since our twins was born he hardly ever drinks and never to excess as we both have responsibilities now - I couldn't put up with this kind of shit now.
Having said that, I wouldn't be going anywhere - you've got three kids and he's the fuck up so he can leave.