I have searched this site and didn't find a question with the specific issue we're facing.
We've tried to teach our dog fetch and came across an issue we didn't know we we're having prior to this and since then have noticed it's not a problem related to fetch training itself. Our dog (7 year old Lab mix... Or shepherd... Or anything really) will go after the ball and get it. She does then run our direction when called but takes a turn just in front of us. After that she will lay down and chew the ball making sure she keeps a certain distance to us. Most times we have to pretty much "corner" her to get close. We are certain that's because she doesn't want to give up the ball. However she displays no signs of aggression, anger, fear or excitement during the process. Once we get a hold of her she gives up the ball easily when we grab it (we don't pull or anything, she let's go when we touch it). Also later we noticed that when we proceed the walk and she has the ball to carry she does not respond when recalled as long as she has the ball.
She loves chewing more than anything but that's not a suitable activity for walks and I'd like to have her running and be involved in play time when on a walk. She has a chew toy available at home that she has access to 24/7 (and I'd like to keep it that way). Giving up the chew toy is not a problem at all. However she won't fetch that either but drop it when called. She is not obsessed with toys. She will let us know she wants the ball when we have it but doesn't do so in an excessive way and is fine when she doesn't get it. The ball is something special for weekend walks and is otherwise out of her reach because she will chew it up and destroy it.
We have tried multiple things such as:
Reward her with a treat when she gives up the ball (after cornering her) or offering a treat in return for the ball; she won't take the treat cause the ball is more important.
Don't bother her at all when she has the ball (no recall and nothing); she will come closer to us and lay down there but still keeps a certain distance.
no recall but walk up to her and put her on the leash to continue the walk not "mentioning" the ball at all; no effect at all visible the next times we tried
making ourselves more interesting by backing off from her after calling her... Cheering, clapping.... The whole thing; it worked two times until she understood the concept.
How do I get my dog to stop walking away with the ball considering the approaches we've tried? And in addition to this (same issue so probably the same answer) how do I make sure she responds when I recall her when she has the ball?