I'm so sorry for your loss. The fact that both happened so closely must have been very hard on you and your family.

The standard Poodle is hypo-allergenic and does not shed. I know there are a few other breeds out there the same. I have read Poodles are very good family pets. I have a Pug and a mixed breed. My daughter has asthma and she does well with both.

We had a discussion about shedding and allergies some time ago. This is mainly about shedding but maybe you can get some ideas.
http://petoftheday.com/talk/Forum3/HTML/000059.html