Soldato
Definitely do this. I had similar arguments with VW when my wife's Golf had clutch issues. They originally gave her a poverty spec Polo, but given that they expected the repair to take over a week, we complained about it. They ended up renting a Golf GTi for her as a long term loaner. As it turned out it took over 4 weeks for them to figure out the problem with her car and repair it.Personally I'd give them the time to sort it out, but insist on an equivalent or better courtesy car in the mean time if there are potentially significant timescales involved.
The whole thing has pretty much put me off VW in the future. I realise not all garages are the same, but the attitude of service managers and staff was that they really didn't give a toss, and having something break on a sub 1 month old car really takes the shine off. Sounds like you've found the same, OP.