Gosh what lovely people on this thread 
The most important think your DH can do for the health of the whole family is quit smoking OP.
The priority has to be to help him do that. On the whole, vapers do far better if they can vape little and often - it's not smoking and the nicotine is absorbed very differently. Especially if he has only recently switched (or is still cutting down the fags) making him go outside away from the DC is likely to lessen his chances of success.
What are your concerns and how old are your DC?
There has been a LOT of research into whether vaping is harmful to bystanders and no evidence has been found. Public Health England, having reviewed all the evidence, have stated: there is no evidence of harm to bystanders from exposure to e-cigarette vapour and the risks to their health are likely to be extremely low.
(actually you might find that whole document useful, it's aimed at workplaces and venues but talks through all the pros and cons of allowing vaping in various settings)
Are you concerned your DC will take up vaping when they are older? All the evidence shows that those young people who vape regularly do so for the same reason as adults - to cut down or quit tobacco. Beyond this, young people are experimenting but not getting hooked. Outside of lit tobacco, nicotine is simply not that addictive.
Maybe ask him to pop into another room to vape if you're concerned and talk to the DC in an age appropriate way.
Well done to your DH he's doing a brilliant thing for his health and the health of the whole family.