New Kitten, Bad Track Record?

Ok. Now, all of you cat lovers, bear with me. I love animals. All animals. But I am a tried and true dog lover. I have two miniature schnauzers, and they are my fur babies. I live in the country, literally in the middle of NOwhere, with my only neighbors being family, and they are few. Naturally, we have mice. I want an outside or an indoor/outdoor cat to help control the mice, and because I was raised in the country, and EVERYBODY had a cat. Outside. It was nice to sit on the porch swing with a kitty in your lap and enjoy a tall glass of iced sweet tea! Anyways, in the past 6 years, I have had 6 cats. Out of the six, 1 stayed. Granted, the grown cats were given to me by people trying to diminish their own populations. But they left. Quick. Like, after 2 days. Half are living at my husband's aunt's house, and the other half at my ex-neighbors (we lost two cats at a location at which we no longer live). Now. I already know what you're going to say. The cat should stay inside. They wouldn't have left if they had been kept inside. True. I understand this. But I have some problems with an inside cat- 1) remember the mini schnauzers? They have never acted aggressively to any other animal, ever. But I already have two animals in my house, and I don't know about adding a third. 2) I have a problem with people who let cats on their dining tables and counters (ew yuck, cat hair in food and itty bitty kitty paws that just were in the litter box on the place where I eat? Gross.). I also enjoy houseplants and the fact that my dogs are non-shedders. I also like the fact that my dogs go potty outside. Where they should. I like to have nice things, breakable things, on shelves. And I want them to stay there. Unbroken. 3) How is the cat going to get to the mice if he's inside?? My husband and I have our house situation controlled as far as the mice are concerned, but our shed? Not so much. I want to have a relationship with my cat. I don't want a cat that isn't going to let me pet or touch it. I want to be able to play with it and love on it. That is why I was thinking an indoor/outdoor cat might be best. So, I guess what I'm wanting are some opinions on this situation, and also, if you are responding positively to the indoor/outdoor thing, what your opinion would be of leaving a window open for the kitty to go and come as it pleases. Sorry this was so long, but I wanted the people that are going to rake me over the coals to understand. Also, know that I already know about getting the proper vaccinations, getting the cat "fixed," flea and tick treatments, so forth and so on. Not my first pet. And I'm a nurse. I know that they need medical treatments and vaccinations. You are now free to criticize. Thanks so much guys.