There is no word るわけ. The る goes with the verb ねて.
ねてる is short for ねている, "[someone] is sleeping".
So what you have here is
ねている + わけ
Without further context, it's hard to say exactly what this means. If you provide more context, I could perhaps say a bit more. However, whoever is speaking is saying that [someone] is sleeping.
If we take a bit more a look at the sentence, we can analyze it's structure a bit more.
First, I'm going to strip it of its formality and leave the けども part aside since you say you already understand that much.
So, what we have is
ねてるわけなんだ
which is just a shortened form of
ねているわけなのだ
The のだ part here is the explanatory の and the copula だ. Often, this portion is not translated into English. But it's conveying an explanation for why something is the way it is (here's where context is important).
わけな is just わけ + な where な is attributive form of だ to be used before a noun. The noun in question is the explanatory の. わけ always feels a bit protean to me. It can mean "reason" or "cause" or "meaning". Here it feels (again we're missing context) like it's just asserting the situation.
If I were to try to translate this, I'd go with something like
Well, she's sleeping.
This is being offered as a reason for why the situation is currently as it is.