Subservient dog agressive in play area

I feel like I've done well with my dog; about a 3 1/2 year old great
dane/lab mix, she is completely subservient to our pack/family, she is
a bit shy with other people, but it seems like she is trying to be
dominant over other dogs. I take her to our local beach several times
a week where she loves playing fetch. I originally thought the
agression centered around ball possession, but it occurred when we were
not playing ball too. The dogs she knows she will behave appropiately
and even play with, but other dogs she will growl and dominate (put on
their backs and stand above) although I don't ever recall seeing any
blood, it mosly scares the owners.

I've started to try to teach her to be subservient; when we are at the
beach, anytime another dog comes near, I command her to lay on her back
(legs up) and stay there even if the other dog comes over and sniffs
her. I'll even rest my foot on her chest to make sure she says there.
But it continues.

What am I doing wrong? Am I making her feel threatened by forciing
subservience? I'm at a loss, any help would be appreciated.

mariann...

I think your dog is scared ..if she was mine I would make her sit ,tell her
she's a good girl and allow the other dog to say "hello " then tell her she
was a good girl again ... Build her confidence as it were ..

Sandy in OK...

Good lord. If you made me lie on my back and put your foot on my chest
every time another person walked by, I'd start getting anxious as soon
as I saw them approaching! Forget about subservience. TRAIN the dog.
Teach her to attend to you when she sees another dog coming. To sit, to
come, to do a trick. And if she's behaving aggressively (or even being
pushy - which is what it sounds more like) she doesn't belong in an
off-leash area with strange dogs where you can't manage the situation!
BroomSandy