Why does she do this?

You can't do anything about what happened to her before you got her , dogs live for now, this is her life now, you just need to get her to realise you are now her strong pack leader. Put her on a lead, long enough to tie around your waist and clip the other end onto her collar( a soft full collar NOT a choke collar), a horse lead rein is good or a 6' double ended lead, you have both hands free so can do all the things you normally do, totally ignore her, no touching the lead, no looking at her and no talking to her, just get on with your jobs as if she was not there. She is a GSD so a clever dog and will get the idea that you are her pack leader and she needs to stay around, without you putting any pressure or additional stress on her. After a week of this you will have a dog that follows you around and never goes very far from you. This type of training is hard for humans to do at first because you are totally ignoring her and humans like to speak a lot but great for dogs as you are not putting any stress onto her, just replicating what her mum would have done (without the lead)remember English is a foreign language for dogs.

I think you are most likely correct in your assumption that she has never learned to be a real companion dog. When you are outside with her, get her to do things for you [teach her to fetch or pick up items], play with her...so that she starts to know that outside isn't for you to do your thing and her to do hers.....but a time to do some things together. Stop every 5-10 mins [gradually increase time - this will only take a couple of weeks at most] and throw a stick, give her a good pat/cuddle or simply just talk to her. If she heads off, call her back in and reward her with your affection. It may seem a bit of a chore, but it won't take long before she becomes fully your dog and will prefer to be close to you. Remember that dogs consider us humans to their responsibility. You must firmly become a member of her pack - then she will 'guard' you. She sounds so independent that maybe she has also been mistreated - she may need to re-learn how to be loved. Your firm discipline and affection will soon show her that she now has a home where she is loved and wanted,

Finally may I say, Good on you for taking in a stray!!!!

I have had a German Shepherd female and they are usually very very 'protective' of their person. Perhaps your reasoning for her lack of this instinct is correct but she is very lucky to have found you and I am sure that you can 'teach' her how to stay close. The key is to make yourself and what you do more interesting than her need to explore. perhaps you can keep her on a long leash with you all day - securing her safely close by whilst you are working horses etc. Always have some treats in a pocket. Bribe her basically! This may take a few weeks to work (if it does work) but having had a little experience with Shepherds, I think something along these lines will work.

Maybe you can get a dog run to let her out. Is she more comfortable in the house? Does she deliberately try and run away, or seem to panic outside? If she is more happy in the house-keep her inside during the day. If she is overly friendly to everyone and everything-she is a good companion. Will she sit and allow you to pet her when you are inside? She just isn't a "farm" dog. She isn't aggressive to the other animals, which is great. She isn't following you around doing chores, because she isn't used to it. But if she is loving, affectionate, etc. as you have described her. She doesn't seem to need much correcting. You can train her to "Come" on command or "stay" She may enjoy her freedom outside, as most animals do. So she wanders.

About how old is she? Since she was picked up as a stray, if she's older, this may not be new behaviour. I have no idea what page wire fencing is, but you may want to think about electric fencing (expensive, and she may learn to break it), or, better yet, try leashing her to you at all times. If you have horses, you probably have one of the extra long horse leads-that'll do the trick nicely for outdoor fun. Just mind she doesn't chew it, as many of them are made of nylon, which can cause dangerous, expensive intestinal blockages in dogs.

Is she fixed? If not, unspayed females are much more inclined to roam.

She may be a little bored, too. While your house sounds like doggie heaven, if you can find time in your busy day, try a little one-on-one, heavy training time. A tired pup is a happy pup! Especially work on getting her to come; give her a tasty treat and lots of praise every time she responds quickly, and sporadically throughout your day call her and treat and praise. She may lurk close just on the off chance there's a num-num in the offing!

Shepherds are working dogs by nature-any chance you can assign her a task? Have her carry a basket, or empty horse buckets...I dunno, get creative with it. Could be fun, for you AND her!

You'll definitely want to address this issue, though. If she's as friendly and cheerful as you say, chances are good she'll just hop right into any old car. Think about getting her microchipped so that if she shows up in a pound or vet's somewhere, they know who to call. I may be thinking wishfully, but I think there's even a GPS chip somewhere, where, when Pup goes missing, you can peek on the computer to see where she's gotten off to. Maybe try consulting a good trainer or behaviorist near you; try asking your vet for recommendations.

Best luck! Thanks for adopting one of our furry friends!

With all that acreage, have you considered ever taking her for a long walk? Dogs connect to people by walking and doing work. She has so much space to run around, you might not consider it. But she's bored most likely. She knows your property and now she's looking to find more to do elsewhere.

Training your dog will be a huge part of your interaction with him for the first few months. Learn here https://tr.im/OlhCJ

This includes housetraining, leash training, obedience training, socialization, and problem solving. In addition to providing your dog with needed skills, this time will also be a great opportunity for you to bond with him. Take the time to really get to know your pet while training him and a loving relationship will easily develop.

Sounds like she may not have bonded strongly with you yet. GSD's normally do not wander far from their master. You could try keeping her on a long lead and going for lots of walks with her (walks are a great bonding activity). Does she like food treats? keep some in your pocket!

Work with her, she her you are her leader by teaching her things, like sit stay etc. talk to her and give her commands often, that combined with walks will help build your relationship. Sounds like she feels she is visiting spend time one on one with her.

she is probably just curious. dogs get bored very easliy i have 4 labs and it's hard to keep thier attention very long. just give her toys or walk her around sometimes. hope i helped.