In terms of going back to the EU....................
In almost everything the EU deals with you have to accept the cards you are dealt with and in the main, they hold a much better hand than any of the individual countries. So in terms of negotiating with the EU they tend to take a pretty rigid line.
What Mrs May has tried to do is find the line of least resistance and that, whilst acceptable to the EU leaders is not acceptable to the MP's who represent the individuals in the UK.
It's pretty obvious that Mrs May doesn't play cards, and in particular poker, or bridge. She doesn't quite know when to fold, bluff or finesse and as a result her opponent is walking all over her. Of course they are going to say there is no movement in their position and that she will find no room to manoeuvre. Ireland in particular are playing politics as they are trying to play the long game and essentially separate Northern Ireland off and make them one whole island nation and of course the UK government really shouldn't be that daft to allow it to happen, but essentially they are.
The only way for her to deal with the EU is say; "ok no deal, we're off, we wanted a deal but what you offer isn't going to work and that is unfortunate, but that's life and your various countries that want to trade with us will now have to go through hoops and taxes in order to deal with us".
I wonder if the multitude of businesses in the EU that undoubtedly benefit from trading in the UK will allow them to do just that?