No, the EU did NOT suggest a border in the Irish Sea. May said what the EU was proposing was "tantamount to there being a border in the Irish Sea", at no point has that idea ever been mooted by the EU.
brexit-and-the-irish-border-question-explained
The EU know better than to suggest a border in the Irish Sea because that solves precisely fuck all. If Northern Ireland is still part of the UK, then the GFA must be honoured and the GFA states that there will never be a hard border on the island of Ireland. It would stir everything up again - Derry/Londonderry is smack-bang where a hard border would be and it saw the worst of the fighting during the Troubles for that very reason - and that not withstanding, many who live in (London)Derry work in the Republic, having to queue at a border checkpoint and have their passport on them at all times is, I'm sure a hassle nobody would willing agree to.
Finally, the DUP. It wants to leave and, obviously, it is anti a united Ireland. How do you propose that circle is squared…?