Uly, just curious: is this a modern 'fairy tale' of some sort? Linguistics and tonal style of the text is somewhat typical of Russian Folk Tales...
Anyway, I'd suggest the following translation: "He divorced his wife, and then all hell broke loose: every day he's tipsy, going through whores as some men go through socks. "

I dare not judge how good PB's translation is (I just like it because it was a rather challenging task). More over, I'm clueless about how you should interprete the trickies part of the snippet - понеслась душа в рай.
I can only say that according to a thesaurus it implies the intense start of an activity combined with an euphoria. So, at least, the use of it in this situation is correct.

He divorced his wife and ... yahoo! flung himself into boozing and sleeping around.

Here we go! здесь, кажется, не работает.😉

Tatiana, I was actually more interested in the use of успевает here. Also does менять imply having a different woman every night?

Paddington Bear, thank you. This was actually offered as an example of the usage of понеслась душа в рай)

Tatiana, Uly, - thank you :)

Anytime 😉