I am confused you don't want a puppy but you can't get a rescue so where are you planning to get the dog from?
An adult dog will not necessarily come ready trained and ready to fit into your family ideal of romping with the kids.
All dogs smell, all dogs moult or will bring mud etc into the house, the dog will not get company from being left with the cat.
Leaving the dog for 8 hours three days a week is a long time - there is a reason the rescues will not rehome in that situation.
Many dogs will find this hard, many dogs will show behavioural issues because of this, many dogs will then have to be rehomed - rescues have been in the business a long time and have seen this happen time and time again (partly why the rescues are so full) - yes there are exceptions but most dogs being left for this length of time is too much.
I will hide the thread rather than read all the comments by people that leave their dogs and say they are fine, they may appear fine but they are not! Just because others do it does not make it healthy or appropriate for the dogs.
If you want scientific evidence of the effect of dogs being left alone:-
dogs.channel4.com
Blackwell, E. J., Casey, R.A. and Bradshaw, J.W.S. (2006) Controlled trial of behavioural therapy for separation-related disorders in dogs. Veterinary Record 158 (16): 551-554
Butler, R., Sargisson, R.J. and Elliffe, D. (2011). The efficacy of systematic desensitisation for treating the separation-related problem behaviour of domestic dogs. Applied Animal Behaviour Science, 129, 136-145
Scott, J.P. (1967). The evolution of social behaviour in dogs. American Zoologist, 7, 373-381.
Nagaswa, M., Shibata, Y., Yonezawa, A., Morita, T., Kanai, M., Mogi, K. and Kikusui, T. (2013) The behavioural and endocrinological development of stress responses in dogs. Developmental Psychobiology, 9999, 1-8.
vetbehaviour.info/dogs/14-separation-related-behaviour/15-preventing-the-development-of-separation-related-behaviour-in-puppies.html
BehaviourVet WordPress blog: Left ‘home alone’: a welfare issue for dogs