I know this will sound odd but in a very strong sense the folk on here are fortunate in that they have been able to get a diagnosis one way or another. The ones in real trouble are those who know they are sick but have no idea what the problem is, hence getting ever more inundated with parasites
with each passing day. So really you've already made the most important step in beating these things and that's knowing that you have them - now we just need to figure what specific critter you're dealing with (and your kids perhaps) and work out the best plan of attack.
I am lucky in that despite having been infected for decades they seem to have kindly stuck to my intestines, so I've focussed on treatments that work there (ie. diatomacaeous earth, mebendazole). There are plenty of other treatments taht will help to reduce the load elsewhere in the body - albendazole for instance kills them everywhere. Starting to treat them will probably ensure that they at least will not proliferate, and the fewer there are the less they can change your body to make things more hospitable to themselves (ie by changing your alkalinity).
BTW - are you doing anything to deal with die-off symptoms? One die-off symptom is being hyper-emotional, though given the situation with your kids we can understand that the tears may be flowing. Taking milk thistle will help your liver to deal with the poisons they release when they die, and l-ornithine and l-arginine will help too in this regard by a different mechanism.
Keep in mind too that if your kid may have felt an itch on their foot taht doesn't mean they are hyper-infected by any means (or indeed infected at all) - its not unusual at all for the parasties to venture all around the body.