I am so sorry for your loss.
You betcha you can train for a 1/2 running three days a week. There are lots of running programs that allow for such a schedule. In fact I only trained 3 days a week for my first 2 half marathons and did ABSOLUTELY fine. I like that you are giving yourself a day's break from running between your runs. If you are currently running 6 miles, I wouldn't rush into 1/2 training quite yet.
What I would recommend is that you go out 16 weeks from your 1/2's race day and then begin your training. Doing too much too soon can lead to a greater potential for running injuries. This will be a great time to just build a solid running foundation so that you don't peak before your race.
I wish you well! RUN SPARK STRONG!