Caz, I am sorry if I sound rude but you are talking complete bollocks about rehoming centres. "Bounce" rates (dogs coming back repeatedly) are much higher at pounds but these organisations don't usually provide the careful behavioural assessment, homechecking, behavioural backup etc that reputable and careful rescue charities provide. There are a wide spectrum of rescue organisations and I am sorry if you have had unpleasant experiences with one.
A great deal of independent academic research has been done on the amount of dog adoptions that break down, and the reasons for this, along with the protective factors that help adoption to "stick". The Dogs Trust, a reputable rescue with widely regarded policies was found in the research to have a rate of adoption breakdown of 14%. Of course, there are many reasons for this, many not associated with the dog e.g. marriage breakdown. A similar study into greyhound adoption found a breakdown rate of only 8% - that means that 92% of these adoptions went well and were supported. This is one of the reasons why I, and others, advise care when picking a rescue and suggest looking for one that provides ongoing behavioural support, and backup. One very high profile national rescue that is based in Wales charges for its behavioural support (£20 per consultation) - something no other reputable charity does.
It's also worth remembering that rescues are always on hand to support adopters. Recently I've been dealing with a lovely lady who adopted two greyhounds from a charity I volunteer for. She has been in hospital recently, and we have been supporting her by providing emergency care for the dogs, visiting her in hospital and it's likely that when she comes out, she will not be well enough to care for the dogs for a while, so they will be fostered by the charity, and possibly permanently rehomed depending on her prognosis and recovery. This lady adopted over five years ago yet the charity is there to support her every step of the way. Eventually, this may be classified as a relinquishment but we will make sure that the two dogs are kept together and find a loving home for the rest of their lives. It's hardly the sort of behavioural meltdown you seem to want to picture.
Many rescue charities do not use kennels at all, and instead use a network of foster carers. Dogs in foster care can be thoroughly assessed, often for a minimum period, and their behaviour with cats, other dogs, children, adults etc can be assessed in great detail. Many insist on a minimum period in foster care to ensure this level of detailed reporting. Many also have quite strict policies on not rehoming with children under 5 - again, to minimise the sorts of situation described in the OP. These blanket policies are controversial, and not all rescues have them, but they do ensure that dogs and toddlers are kept well apart.