Young children (and the unborn) tend to be at higher risk from environmental toxins that are adults. The risk you will face depends on both the type of termite and the type of treatment. that’s being done. Basically there are three types of treatment.
The lowest risk are with baits for subterranean termites which use hormone-like chemicals to interrupt insect growth. At the rates they are applied, these are very low risk to people (and anything else that hasn’t got its skeleton on the outside).
Next are the fumigant gases uses when a building is tented for drywood termites, these evaporate away almost entirely and pose little if any risk to you (or any returning termites) if the gas is properly handled and vented. Make sure that everything has enough time to out-gas. Some furnishing (like rubber cushions) may need a longer time. Your technician will advise.
Last are the straight poisons (termiticides) which are usually applied to the soil but are increasingly used indoors as well. These always pose some risk, especially if poorly applied. You need to find out the identity of the toxin and look it up on the next. Search on ‘toxicity of” and then the chemical name (not just the product name). Termiticides are not all the same, and some termiticides are best avoided because of their risk profiles (such as organophosphates and still in some countries, organochlorines). Nearly all will persist for quite some time, and this is where exposure is likely. Make sure you are away when the chemical is placed and don’t return until after the recommended period. You will need to do your own research, but from manufacturer claims, it looks like the current least-toxic soil termiticide is chlorantraniliprole, closely followed by imidacloprid. Many will dispute this. The biggest risk is chemicals sprayed on the soil around the building where your child plays and will inevitably pick up and ingest some (kids eat a lot of soil). Sometimes, chemicals are applied as dusts or foams into wood or wall cavities. As long as any excess is cleaned up (and you don’t open the cavity), the risks are considered low. In a few backward countries, like Australia, the government allows for arsenic dust to be used. Arsenic dust is highly toxic, doesn’t break down and isn’t not more effective than the modern alternatives. It should never be used. If you find unexplained red, blue or white dust in termite-eaten wood or their old shelter tubes, please consider it dangerous until proven otherwise.