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I grew up in a fair-sized single-family dwelling. Three bedrooms, one bathroom, living and dining rooms, and kitchen. Good sized back yard with a 100+ year old Indian Maple and a 30+ year old mulberry tree. There were four boys, two older, and two younger (I'm the older of the younger kids, we're now 38,37,27,24).
Don't move. Despite being able to keep them in the same schools, moving is hard on kids. I have great memories of my childhood home, and I can't imagine the differences it would have made in my life if I hadn't had that stability. Expand your home. Sacrafice a little bit of yard for a good study. Consider adding a floor to the home. If you have the money to buy a new home, modifying this one is likely doable as well.
Build a treehouse, make it beautiful. Tell your kids it's their private space. Let them have it to paint and play in. Tell your kids the study is your and your husbands private space. Let them know not to bother you in there. Agree that you won't intrude into their house if they don't intrude into your study.
Teach them the value of privacy, and of shared space. When you're together, do things together. When they go off to play, take time to enjoy your space. Go outside and spend an hour beneath the tree, listening to your children play, or reading. Hang a Hammock!
Carports are good, but ask yourself why you need a place for your car. What is it about the idea of a garage or carport that makes you feel bad not having it. Is it just being out of the weather? Is it not having to wash your car? Are you looking for a dark, separate space (Basement/Garage) in which to put the things that you don't like about your life? The clutter? The aggravation? -- Before you go looking for places to put skeletons, know what skeletons you plan on putting there, and decide if it's good to do it.