I can see your concerns, but there are positives as well as negatives.
One thing your husband would have to consider is whether he would want to walk the dog for at least half an hour and at least twice a day - in all weathers. If he is prepared to do that, he will get a lot more fresh air and exercise and, if he is missing the social element of being at work, he may well feel more part of the community through meeting other dog owners and stopping for a chat.
A dog is, in my opinion, a wonderful - and often amusing - companion. It has also been proven that stroking a dog (and presumably a cat) reduces high blood pressure and has other physical and mental health benefits.
If you do not have a friend or relative who would be willing to look after your dog when you go away or you would find it financially difficult to put the dog in a kennel, I can see that that might be a problem. If you mainly holiday in the UK, there are hotels who accept dogs and good self-catering companies who have a small range of dog-friendly accommodation. We nearly always take our dog away with us.
Has your husband considered that there are other expenses to be borne in mind - insurance, vaccinations, food, flea/parasite treatments, etc. etc. and all this can add up to a fair amount over time?
Is it definite that your daughter and granddaughter have an allergy to dogs - even short haired dogs?
I have several friends and family - particularly Asian friends and family - who are generally quite scared of dogs but who have, gradually and over a period of time, come to trust and like our dog once they see how friendly and gentle he is.
I sense, though, that you're pretty adamant about not wanting a dog and so - for everyone's sake, including the dog - it may not be a good idea.