Gorgeous puppy indeed!
I have a 13.5 week old GSD, and a 12.5 year old chihuahua cross pom who is also very spoiled. It's ok to have a spoilt brat when they're that small you can live with it...
I'm NOT an experienced trainer, and I have had some problems with the two getting on. In addition to everything my chihuahua/pom wasn't well socialised with other dogs, and she only just tolerates other dogs.
Anyway, I put off getting the GSD for years because of this, but I've had some security scares (I live alone in the bush) and the little dog is getting deaf so I took the plunge.
Firstly they got on a lot better than I expected. Somehow Coco sensed this dog was here for good and took on a different attitude. Second I kept the GSD (Sasha) crated when around Coco. This helped a huge amount. Also I maintained Coco's role as primary dog, so if anything I increased her pats etc. I may be imagining it, but I felt that after about a week she realised that she wasn't going to be usurped in her position, but that we were now an extended family.
I feed them separately, and Coco has an exclusive protected place on the couch and in her nest bed, that I have trained Sasha "relatively successfully" as off limits.
The biggest problem is play. Basically I cannot let them play unsupervised. Sasha is just too rough - way too rough. She is still a baby and has no idea how to control the roughness of her play. I also work to predict what is going to happen. I've been doing marker training for about 3 weeks with Sasha to get her to be in a calm state, and to watch me. It has really worked.
The most surprising change has been in Coco. In the first 2-3 weeks she became really badly behaved (she is moderately trained and obeys all major commands), it was like she decided to perform for the puppy NOT for me!!! Anyway once I realised what was happening I sorted it out very quickly. - now she is back to obeying but It's like she has become a completely different dog! She was a fussy eater, I'd home cook her meals - human quality balanced diet... now she's eating raw kangaroo, pigs ears and stealing marrow bones off Sasha!! Unbelievable.
Because Coco has always been very dominant she holds her own with Sasha when Sasha is calm (30%) of the time :-) But she is in real danger when Sasha is in manic play mode. I'm always at an arms length when they are playing. The initial stages are great and I want to encourage them, but need to step in immediately it gets too rough.
Also when I'm training Sasha, Coco feels left out and imposes herself into training. I'm finding that I can use the competition to my advantage IF i manage it. I immediately stop any overt competition between them and both know that it will not be tolerated.
I also use a lot of time out - since both are very social, and that short '"out-ing" does wonders.
Oh yes and probably the most important thing of all. Thanks to the advice from people here, I have had Sasha on a tether. When I took the tether off after the first few days, she really went wild, and I had great difficulty controlling her. Back went the tether, now for about 2 weeks, and she is MUCH MUCH easier to manage in every respect, plus our respectful bond is much stronger. I really recommend that you tether your GSD at home during the day. It will be your wife who does this, but I think it will make for a much more manageable situation. On tether it is very easy to direct the puppy. With two dogs at home running around I was going mad. The tether introduced order.
It is however slow going and at times a few days have felt like a few weeks. However now heading into our 6th week, things are much better. Routines established, rules set down, and pecking order sorted out - Me, Coco, Sasha... LOL
I realise that I've probably outlined a range of things that are "wrong", but I thought my real and current experience might be of use to you. BTW In preparation for Sasha, I have read about 15 of the best Dog books I could find, (I'm academically inclined). But none of them really prepared me. Of all the resources, I have found the Leerburg material and this forum the best.
Good Luck to you, and as someone said to me on my first post here - Enjoy the ride!!
Mara