A fenced in backyard has nothing to do with how much exercise you can provide a dog. I have a fenced in yard and the literal only thing I use it for is putting Eden outside without supervision LOL. All of her exercise happens outside of the house. I mean sometimes she’ll get a ball thrown, but Eden will tell you that that’s not enough exercise for her either lol.We could exercise her more but we don’t have a fenced in yard and I don’t trust her off leash in a park or on a trail.
If you don’t trust her offleash, get a long line, 15-30’ should be good. There’s a little bit of a learning curve, but you’ll be able to figure out. For most adolescent dogs, a leashed walk a few times a day is not sufficient exercise- they need the opportunity to do what they want in nature. Kaizer would just run and run when he was off-leash - he’d go 5 miles to my 2. Eden never goes more than 30 feet from me and prefers to wander through the woods, smelling alll the things - she probably goes like 3 miles for my 2. The end result was the same: quiet, happy dogs. And when you’re out there, work on that recall so you can eventually trust her off leash.
Truthfully, it sounds like she needs to learn how to settle inside (which is a common issue imo) and that’s not possible without making sure her exercise needs are appropriately met. Meeting exercise needs doesn’t have to take up hours of your day if it’s the right kind of exercise. Eden is an active dog, and her exercise is an hour-long off leash walk or 20 consecutive minutes of swimming in a pool. We do some casual training almost everyday for 5 minutes/day (maybe twice a day if we have something coming up). Occasionally we throw a ball in the yard for like 15 minutes, but not religiously. I think you’ll find her early morning wake ups will start to lessen in frequency if she gets exercised appropriately too.