I really hear you on this issue. I'm a Building Performance Consultant who also deals with EBV and very sensitive to chemicals, VOCs and molds. I too disagree with the use of tenting and gas for many projects. However, on my house, the termites are coming in from multiple locations, so there really is no choice than tent n'gas.
However, if there are only localized problems such as a particular corner of your house, there are spot treatments which including electricity, Orange oil and heat (all non-toxic). The ability to use non-toxic methods really depends on how bad the infestation is and how many locations are affected. The other issue is that not all pest control companies offer the non-toxic methods. I live in an area where the closest company that offers alternative methods is about 60miles away.
The other thing to think about is if you see evidence of termites ie. droppings or bodies, the problem has been there for at least 5 years. It takes 5 years for a colony of termites to get to the point of showing its presence on the exterior of the building. When landlords hear or see the problem, they freak out and take the most aggressive action. We are coming up to Spring which is when termite populations explode. So now is the time to deal with it.
For your health, if there is someplace you can go for a week, a day or two past the time they say you can go back, your health shouldn't take a nose dive. In my opinion, everyone with health problems should have at least 1 Mother n' Law tongue, plant. They really help clean the air, pump out oxygen and easy to clean and care.
That's my 2cents.
Thanks, they had someone come to inspect the damage and according to them, they need the house to be tented. I do plan on staying somewhere while they do it and move everything that I think could be affected (clothes, mattress). I just want to be careful cause even though they say it dissipates, I want to make sure the things I have aren't given off gases in the long term, it really is speculation though but I rather be safe then sorry. I do also plan on getting lots of plants and possibly salt crystal lamps for the future cause I am going to be living there for a while.