Ok, there's enough information on the problem now.
Apparently, soldering 20 feet away from a cooking area, on the same level of a dwelling, even with doors in the way, with a common airspace, single HVAC, and kids around is a no-go; don't do that.
However, in a suburban garage, attached or unattached, soldering fume risks are much more manageable there. You're in California, the garage door can be kept open while soldering. Assuming the garage is owned rather than rented, and is a wood-frame building, you could add a 2-inch hole near your workspace, add in a dryer vent on the outside, and complete a solder fume extraction system with a $2K budget.
I wouldn't do that though, it's unnecessary.
Given the garage's isolation from the living space, proper ventilation, perhaps a shop fan in the garage with open door, it seems that would suffice. I use the equivalent of the Hakko 493 Smoke Absorber, and you could choose whichever model you want.
Solder and solder fumes are dangerous for anyone, particularly young children in a home environment.?
In a managed garage environment, I wouldn't expect solder and solder fumes to be terribly more toxic than a combination of fuels, oils, paints and thinners, lawn chemicals that may be stored there as well.
It is lead, not cesium. Keeping a clean garage and home and managing the risks there should resolve this problem.
