I'm in the same boat. I love the woodstove, I HATE the mess.
I've finally got DH to habitually open the stove door *slowly* but he still won't stop blowing on it in the mornings to get it started. That just sends the ash dust everywhere. Drives me nuts. So I try to make sure I start the stove by using draft alone to keep the dust IN the stove.
Otherwise, I vacuum 2x/week and dust once a week to stay on top of it. Oh and my vacuum has a hepa filter.
DH and I - totally winging life with our four children, DS1 (6.5yrs), DS2 (5yrs), DD (3yrs) and DS3 (1)!