One who transgresses Shabbos publicly has the status of a Gentile (Shulchan Aruch Y"D 2:5 and Shulchan Aruch Harav on it). Furthermore, Jews are forbidden from having relations with Gentiles.
That being the case, is it permissible for a man have relations with his wife who publicly does not safeguard Shabbos (despite having safeguarded Shabbos in the past)? Additionally, can she be trusted as regards the laws of Niddah (i.e. family purity)? (Can the husband assume that she did not have relations with another man, so she is not forbidden to him because of that?)
Any souces on the subject will be appreciated.