My GSP doesn't fetch under normal circumstances either ,though I know lots of ones that do. We found out about a year or two ago that he only plays fetch inside with certian objects (such as his jingly ball) and he will ONLY play fetch outside if it is warm out and he will only fetch outside with his dead tennis ball, which is a ball that used to be a tennis ball but he has ripped the green cloth completely of and the ball and it is almost in half. I don't have any advice for you on that because we have tried everything and the only reason I think he plays fetch outside at all is because he had buried that ball himself and then dug it up two years later. (maybe it's the earthy smell) As for the submissive behavior, no clue. Maybe try spending lot and lots of time with her. My GSP has always been a super friendly boy.
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