As I understand it, a successful no confidence vote would trigger a Tory leadership election. Whoever wins, most likely forms a new government with the DUP. However, this all would take time. Valuable time they need to try to re-negotiate a proper deal. A no confidence vote IMO ends up with one of two things, a hard Brexit or trying to extend the Brexit date rescinding the Article 50. If they did the second one I think that would trigger another referendum which IMO is a ridiculous outcome.
From what I’m reading, my opinion is the best option is she wins the no confidence vote but just barely. This would most likely force her to resign and an interim PM could be installed immediately with a vote on Tory leadership to follow. Whoever they install as interim PM most likely would win the election. If they installed a true Brexiter as the interim, I think this person could go back to the EU with a bold new plan to negotiate the Brexit. Neither side wants a hard Brexit (though for the UK, imo it would be far better than the current deal) so I can see a deal hammered out more favorable to the UK’s interests.
The need the approval of most,if not all of the EU countries to extend the Article 50 drop dead date. I don’t see that happening.