Sorry to come to this thread late in the day, ROSABELLA, but having been owned by cats for the last 50 years and a member of Cats Protection, I do have some experience of their personalities and attitudes.
This cat appears to be way out of the norm curve for aggression and this should be your immediate concern for all your family, your dogs and most importantly the new baby.
If kittens are not handled correctly in their early weeks ie: play-fighting back with the kitten instead of distracting with toys, or are from a feral litter, natural aggressive play behaviours continue into adulthood and behaviour modification becomes more difficult.
Cats Protection state: " Cats that are aggressive can be very dangerous and veterinary advice should be sought if a cat is persistently aggressive to humans".. Many causes from over exuberant kitten play / a medical condition /fear.
As this cat appears to have been aggressive from the start it is doubtful that , at this stage, behaviour modification would help as it is a long, difficult challenge . Your son says the present behaviour is due to a change in environment but it would seem that it was equally predisposed to random attacks both on them and visitors its previous, permanent home so this is hardly likely to improve in the present circumstances with the added factor of dogs.
Has your son consulted a vet to ascertain that the cat is not suffering a medical condition, surely this aggression would have been seen in the surgery when attending for annual vaccinations?
Sadly it does not seem likely that this cat will ever be a cuddly domestic pet , perhaps re-homing to an outdoor environment is in its best interests. Cats Protection would advise.
In my view you have to put yourself and your dogs first and several other posts have given sound suggestions as to perhaps talking things over on neutral ground, or assisting them with alternative accommodation if they cannot bear to part with this damaged cat.
I feel for you all - the cat included as it is obviously very unhappy.