First, I'm so glad to see that you are really thinking this through. Dog ownership is a big commitment, and often changes your life in ways one can't imagine.
One thing I always tell prospective adopters - never, ever bring a dog into your life primarily because your child wants one. You, the adult, must want the dog for yourself. Children grow up, change interests, leave the house - the dog will be yours.
Now, if you yourself want a canine companion, if you yourself feel your life isn't complete with out a furry friend by your side - and it just so happens that your child wants a dog too - then that's something else entirely.
The question is not only is a dog right for your family, but more importantly: Can your family provide what the dog needs?
For most dogs, living outside is not a good option - not the least because your neighbors. Should the dog bark and you are not right there to quiet it, you could find yourself facing noise complaints, and your dog could become the victim of a neighborhood revenge campaign. There are also very specific regulations in the new TschV as to accommodation for dogs kept in runs; do be sure you study the law - and don't forget that you'd likely need building permission to put up a dog house/run.
Most dogs crave the company of their people - they are social animals, living apart from the family is simply not fair to most individuals. Note that I said 'most'. A dog needs interaction, needs training time, play time, hanging-out-with-his-people time. Think of the dog's mental as well as physical needs.
But wearing my rescue hat, if your wife does not want the dog in the house, that sets alarm bells off for me. Lets face it - dogs are messy. It's part of their charm, it's part of the package of dog ownership. (But the mess is easily cleaned... ) I'd have some serious discussions with your wife about what she can, and cannot, tolerate before going further.
(The rescue I volunteer with would not consider anyone who wished a dog to live outside. Other rescues may not object.)
When my dogs were young and healthy the costs were insignificant; a few thousand a year** for training activities (Swiss prices ), perhaps 500 a year for medical expenses, and depending on the size of your dog, anywhere from a couple of hundred to a thousand a year for food. Holiday dog care is expensive though: for instance, ca 200 per day for in-home care, ca 40-75 per day for kenneling.
Now that mine are older medical expenses have become rather hefty - care for one of mine regularly ran over a thousand a month at the end. Granted this was a short term issue - but one does need to plan for some significant expenses at some point over the course of a dog's lifetime. Accidents happen, surprises crop up - it's very easy to run up a four and even five figure bill.
Your most pressing problem will be finding dog care when you travel - it is difficult to find dog sitters/walkers qualified and working legally under the new TschV. You put yourself and your dog at risk by employing someone working illegally - but the new law has made it very difficult to qualify. It's a big problem these days. If you travel a lot, I would not get a dog until you have secured reliable holiday care. Competition for kennel space is keen during traditional holiday periods, some place are even booked a year in advance.
Given that you work full time, a puppy is not suitable. A puppy needs someone home all day - he should not be left for more than a very short time in the first 6 months. And he still needs someone home most of the day for the first year. An adult dog would be a better choice for if you are not at home during the day.
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Would I recommend that you get a dog?
Now, my dogs are everything to me. I spend most of my time involved in things canine, I wish everyone could know that same joy a happy waggly tail can bring into one's life.
BUT - again with my rescue hat on - I worry about what you have written about your wife's feelings, and about your own reservations. Given your priorities, I wonder whether your family is ready for all the complications of dog ownership at this stage of your lives.
I would suggest that you - and your wife - take the theory portion of the SKN now, before you go any further. (You are required to do this under the TschV before acquiring a dog, and you are required to complete the practical training part within the first year of ownership) And then have a long hard think about what a dog needs from his people and if your family can offer that at this point of your lives.
If your motivation is largely driven by your daughters desire, as a sort of testing-of-the-waters, why don't the two of you volunteer as dog walkers with a rescue? (You would have to be the volunteer, your daughter is too young - liability reasons.) That way, she could see what it would be like making a commitment to a dog - and you'd have the immense satisfaction of doing a good deed at the same time.
Wishing you all the best.
** ETA re: training costs - The mandatory training classes, the Sachkundenachweis theory course and then the SKN practical course, run ca. 100-150 per course. This is a one-off requirement. (Per dog, that is.) On-going training is optional (but highly recommended ). My figure above includes a yearly abo with my training club for Familienhund and Team Training classes, as well as the sports stuff we do. YMMV.