I'm a maintenance engineer myself and busy with my MBA courses with the following strategic question: what maintenance can be outsourced or not. I was wondering if Lego does all maintenance of the molds in house, as the molds are the core of the product and the essence of what makes LEGO unique.
Moulds are maintained in-house.
As you say, the moulds are at the very core of the business of the LEGO company and are thus treated with all the seriousness you can imagine. Considering also that some moulds are in effect trade secrets by themselves (especially for parts which aren't publicly known yet), LEGO wouldn't want any of them to exit the company. (It's been said that retired moulds are embedded in concrete of new buildings, but that's probably an exaggerated version of "they are destroyed".)
If I remember correctly, National Geographic's reportage on LEGO (in a serie on ultimate factories) showed some very interesting insight on the moulding process, including the making and cleaning of moulds, which I'm certain will be interesting for you. You can find these on YouTube; in particular, watch the interview of one Finn Kirkegaard at the beginning of part 2. You'll also notice that these things are absurdly heavy, which would make the transport of them an issue too.