
I think firstly that your decision of going back to basics is absolutely on the right track :) Secondly, I've personally always found bitches a little slower to fully house train than males (although no doubt some folks have had the reverse LOL).
You say she has been to the vet - was cystitis ruled out? a urine sample taken?
At just 16 weeks she is still very much a baby and it is possible that she has made the wrong association between praise and going outdoors. Patience, 100% attention and equal measure of consistency are likely to be your best bet I'm afraid.
As to this possibly being a submissive behaviour - not IMO impossible but less probable unless of course she is showing other submissive behaviours such as going belly up on your approach or her urinating is more a release of a dribble of urine which can be a submissive sign too. Have you concentrated on ignoring accidents and praising the odd times she gets things on the button?