It could also just be a coincidence too that just because the sister had it doens't mean the baby will get it. Everything you described is still totally attributable to teething. The fact the rash is around the mouth and on the bum would never have me suspecting hfm disease - yes if the sister had it maybe and I see where you are coming from. But does it not start as blisters on the hands, feet and mouth first - hence the name. Rash around the mouth and not in it is more likely from drooling and acidic reaction to foods as well as the bum rash and all of that is because of changes in the child due to teething. Hopefully for everyone's sake it is just teething.