I met DDog at approx 1y2m old. Info is sparse, but I gather the home where he was 8w - 12m only took him on 10 min walks around the block, though there were other dogs in the house. So, not too dissimilar a situation to your dogs'.
I initially thought DDog was lead reactive. Turns out he was a frustrated greeter. The difference is the emotion behind it - if its about fear (reactivity) or a dog that is frustrated that it can't go and say hello to the other dog (frustrated greeter) and ends up lunging, snarling etc. It can be hard to discern which emotion is behind it if you're not a professional, though it's common for a frustrated greeter to be fine when off lead with other dogs but a reactive dog to have a meltdown in the same situation. DDog's frustrated greeting has largely disappeared now, almost certainly due to having sufficient exercise and off lead doggy social contact, but if your dog is genuinely reactive then seeing lots of other dogs will only make things worse.
Just to make matters more complicated, DDog is reactive towards a more esoteric trigger - motorbikes. As pp alluded, this is something that is more managed than cured - but we have made great strides with the help of an APBC accredited behaviourist (and lots of liver pate rewards) and can now usually see a motorbike without a meltdown.
I wouldn't be overly concerned about your daughters unless there's something you haven't mentioned; dogs that are reactive towards other dogs don't normally have the same feelings about children, though of course you should never leave a young child and dog unsupervised, and I would be very strict about DC behaviour around DDog. The one thing I would be aware of is that sometimes reactive dogs can do what's known as redirecting. In essence, they end up in such a frenzy that they turn around and bite the nearest thing without really even realising they're doing it. DDog has, on a handful of occasions, bitten everything from my shopping bag to my lower legs when he saw a motorbike (puncture wounds not requiring medical attention only). He meant no harm to me, it was simply that my bag / legs were the nearest thing. If you walk with your DC, and you think that redirection is a risk, you may like to consider muzzling your dog for peace of mind.
I would really recommend seeking out an APBC or CCAB accredited behaviourist sooner rather than later as the earlier such behaviours are caught the easier it is to improve the behaviour. I say APBC or CCAB accredited as there is no regulation of the industry whatsoever (ie literally anyone can call themselves a behaviourist) but those two qualifications are recognised as being gold standard and will help you to avoid the awful ones.