You are exposing yourself to untested, unregulated chemicals. It is unclear if it is absolutely safe as there are some trace chemicals in the vapour; however, it is almost certainly safer than smoking.
The risk of electronic cigarettes is related to the composition of the liquids they use. The safest will be those which use the least number of compounds. Flavourless liquid being the safest since it’s just vegetable glycerine plus or minus nicotine while tobacco smoke has 4000 to 5000 known compounds in it. Experienced vapers make their own DIY liquids to know for sure - and to save money.
The real reason not to vape around children is it sets a bad example and encourages them to start vaping. Children model the behaviours of their parents. If they see you vaping, they may associate it with being grown up, and vape to gain the same association in themselves. They may grow accustomed to it, even addicted to it, through you.