It sounds more like your are mildly alcohol-dependent rather than alcoholic. Alcoholism is when your drinking negatively affects your life and those around you.
Dependency can manifest as a result of self-medication of things like depression or anxiety with alcohol, because it makes you feel good temporarily. The problem is alcohol is also a depressant and makes you feel worse afterwards, making you want to drink again.
I'm saying this because you sound a lot like me (minus the kids, and I was drinking nearly a bottle of vodka four or five nights a week). and I realised I stopped drinking to have fun and socialise and started doing it alone and heavily to self-medicate my depression and anxiety.
I've taken steps to really cut down lately and have started to explore other ways to address the problems I've had recently.
In your case though it sounds like you are self-aware enough to know maybe you are drinking too frequently (though the volume doesn't seem so bad in my opinion) and have stopped drinking for periods before.
I'd honestly say you have a mild alcohol-dependency, not alcoholism.
Alcoholics tend to not be able to stop themselves drinking, will refuse to admit they have a problem, will fail to live up to their responsibilities and even go so far as to hide their drinking from friends and family very well.
This doesn't sound like you.