Not sure what you mean by Dragons teeth ? I can sympathise tho as I have a problem with Celandine over running my garden. When I move any plant to a new clean space, I try to wash the roots bare and pick out any "baddies" before transplanting. Aquilegias don't always like this treatment tho and it can be almost impossible to catch every weed.Also of course you are limited as to what time of year you can do this.
Another method is to pot up your Aquilegia as cleanly as you can and then wait until the offending weed shows it's head........when you are sure each one has germinated, you can clean again as above. Not perfect by any means but worth a go if you have some nice plants you want to save.
I will be more than interested to see other solutions (not just weedkilling as that means spraying the whole of my garden ) but wish you the best of luck in the meantime