Have you tried getting her to use her mind, to play?
Like hide and seek
Like get her a new toy like ragga (that is only used for hide and seek) start by hiding it where she can sort of see it like behind a table leg
Then make it harder each time
When she finds it, make huge fuss of her
Then hide it again a bit harder
Just do it about 3 or 4 times at a go, so she doesn't get bored
You could start doing it when children are in bed or at nursery/play school/school
When she has got hang of what "seek" means then you could try during day
After a few days you could try this before she does the aggressive stuff after your DH has gone back to work
It will get her to use her concentration and is fun
After she has learnt what to do then you could get 5 year old involved in hiding the ragga, obviously with you there too
Put the puppy in different room while child hides the ragga then open the door say seek
I realise you need to find a new home but this might help while you are trying to get a solution