I typically run four to five 5K's and at least one 10K each summer, and I run 2.5 - 4 miles every morning, June through mid-August. I'd really like to try my first half marathon this summer, in late July or early August. I also need to really tone-up my arms and shoulders. If I work diligently on both (training for a half, and "building" upper body muscle) at the same time, can I achieve success for both, or do I risk sacrificing potential quality in one or the other?
You should be able to do both. Take a look at the April 2014 "Running Times", page 22, which specifically addresses this general question. I hope you run the rest of the year too. You may find it beneficial to start doing one longer run each week, getting to 10 or more miles a couple weeks before your half. Also rather than running "every morning". I hope you consider cross-training or resting at least one day a week.
Absolutely you can do both. Regular strength training will only help your running. As far as strength training is concerned, allow 72 hours between training sessions for the same muscle groups. I am looking to establish an online training business as it's more affordable and allows you to train people that are far away ( I am a certified personal trainer with American Council On Exercise) so if you would like help, let me know.