Taylor Frankie Paul is sharing custody of her son with baby daddy Dakota Mortensen amid an investigation into claims of child and spousal abuse ... TMZ has learned.

Sources connected to the situation tell TMZ ... the 'Secret Lives of Mormon Wives' stars have not seen or spoken to one another in three weeks, ever since a heated argument that allegedly turned physical and resulted in Taylor calling police.

Taylor and Dakota have a son, Ever, who turns 2 this week ... and we're told they are sharing custody as the Utah Division of Child and Family Services conducts an investigation. It's unclear which parent -- or both -- are being investigated.

Our sources say things are so icy between Taylor and Dakota, they aren't handling custody exchanges ... and are instead having other people step in to transfer custody of Ever from one parent to another.

As we told you ... 'SLOMW' season five production is on ice as the drama plays out, and Taylor and Dakota have been ordered to undergo psych exams.

Taylor's also starring in ABC's "The Bachelorette," which is set to start airing later this month.