I have come up with the same information as the OP - that an LLC owned by one person, or a married couple, is considered a disregarded entity by the IRS and there is no separation between the owner and the LLC.

Immediately after the 1031 is complete you can contribute the new property into different entity with out triggering a tax consequence.The exception to this is if your LLC is a disregarded entity meaning it is a single member entity and you have not elected for it to be taxed as a partnership or corporation and it does not file its own tax return.  

Our LLC was solely owned by wife, and therefore a disregarded entity.  

So on the sale of the property you put $23188 from equity in your pocket disregarding any sales commission or other selling expenses.  

This would make the SMLLC "disregarded" for tax purposes2.

Personal use also includes time spent at your place by another party under a reciprocal sharing arrangement (“I use your place in exchange for you using my place”) whether the other party pays market rent or not.Days devoted principally to repairs and maintenance are considered days of vacancy and are disregarded, even if family members are present while you work away.The tax drillVacation homes in this category are treated as personal residences for federal income tax purposes.

Generally, it is best to have buy and hold rentals in an LLC taxed as disregarded entity (for multi-member LLC, taxed as a Partnership).

Disregard.

Disregard my first statement. 

Disregarded means that it is ignored for income tax purposes and treated as if you acquired the new replacement property as an individual for tax purposes.