As Velma said, it doesn't mean it's wrong.
One thing to keep in mind, in times of upheaval for kids is that they are looking at you and your reactions.
It is sad that they are unhappy right now, but, of course, kids don't know the whole story and they certainly don't know what the future would look like with an alcoholic.
The idea of rehab to kids of that age is obscure, I'm sure. They don't really know what alcoholism is and they don't really know what rehab is. Perhaps explaining to them that even if their dad went to rehab, that doesn't mean he will no longer drink. I do think it's important to have age appropriate talks about alcoholism, but perhaps these concepts right now are a bit out of their understanding.
There are age appropriate books that can help, I've seen many on Amazon, so that might be a good place to start?
Sometimes you have to make decisions that kids don't like and that's a fact. They don't know what this is about.
They will take their cues from you. If you look and act sad and worried (for them) they may misjudge that as sadness over dad leaving. You all will be fine, but it will take time. It's very important they know about the divorce and why it happened or you could very easily become the "bad guy" here. Don't hide the truth of it?