
Hi Nicky,
TBH I would strongly advise against you taking on a new canine companion from any source until your children are significantly older, upwards of 7 years.
Keeping an eye on two such young children is time consuming enough without the added pressures of raising and training a dog - which, IMO, should be from puppyhood with young children when in a breed you're unfamiliar with and, down to practicalities, have limited time to give dedicated attention and training.
Rescue centres/societies come in as many shapes, sizes and questionable abilities as the dogs themselves. In view of your very recent tragic experience, I think it's neither in the interests of your family nor any 'second chance' dog to take such a gamble for a few years yet.
If you're truly missing the experience of enjoyable walks with doggy company then perhaps when the children are at nursery you could volunteer to do walking and some basic manners training at a local rescue centre which would be useful to the dogs there in finding a new forever home and would I'm sure be very satisfying to you too - and all without the many concerns of having a new resident :)
I hope your daughter's injuries, physical and mental, are improving.
HTH,best wishes,
Teri