Your wife has a good point. If going away overnight is important to you (and sounds like it is to your wife) then you
should establish a plan for how you're going to take care of your critters before you actually get them. Make friends with the neighbors beforehand and see if one of them has a responsible teenager or something you can hire to come over and do that. Most adults I know are too busy to take care of someone else's animals, but might be able to do a trade (you take care of their animals while they go away).
If you want the goats for milk, this complicates things. This really chains you down to morning and evening milkings, and not everyone will know how to milk a goat, and you won't trust everyone to do it for you either, as improper milking can really mess up their udders, or lower production if they don't know how to get all the milk out. And too much grain, of
course, can make them very sick. I don't even trust my husband to take care of my goats, but maybe he is a special case.
You might find when you have animals that you don't really want to go away, unless you can find someone you really trust to care for them. They're kind of like kids in that way.
I've had 6 goats (2 milking) for about 6 months, and am now wishing I had done a little traveling before I got them
Because now I am pinned down for the forseeable future. But then again, I love having all the fresh, organic milk, and am so glad to have them.