They might not tell him but he would almost certainly think you told them. And it wouldn't help him get help.
Withdrawal symptoms: if he's not drinking all day (or pretty much all day) every single day, he may not have the degree of physical dependency that causes them. DPs ex is alcohol dependent, she drinks at least 2 bottles of wine a day, a lot more at weekends or on holiday. But she doesn't have a drink until 5-6 pm on working days, is usually passed out pissed by 9 or 10 and she almost never gets hangovers or the shakes or anything.
Or he could be drinking just enough to keep them at bay. The husband of someone I knew was always really bad tempered every morning until he'd been "out for a walk". She later found out that the "walk" was to the local convenience store where he'd buy a small bottle of vodka, and drink it on his "walk". He'd return in a much better mood.
Your DH is being "nice" because he doesn't want you to leave. That's a big incentive. But the strain of being "nice" and not drinking is making him "grumpy". I know he's not abusive, but it's a bit like abusive men who can be "nice" for ages ... until the day they're not.
I wouldn't be surprised if, some time in the next few days or weeks, he'll get so grumpy that he'll provoke a row so that he has an excuse to go out and get pissed, and you know what? It'll all be your fault, because he'd been making such an effort and you didn't appreciate it.
If he really wants to change and stop drinking, he'll realise he needs to do it on his own. Go to AA or some other local group, get some counselling, therapy, whatever he needs. Just keep telling him that and give everything else the "grey rock" treatment.
You need all your strength for yourself and your kids. You can't do this for him. It's not a problem that can be shared in that way.