OP needs to go read the case I posted in the original thread.
The key is that Arkansas considers it to be cohabitation if the people share a residence. It doesn't matter if the children spend the night in the house when the paramour is present, if she stays in a hotel when the kids visit, if she's NEVER around them at ALL. If it's her LEGAL RESIDENCE, then dad is cohabitating with her.
In the specific case I posted, Mom had been ordered to cease cohabitation with her girlfriend. The girlfriend had begun staying elsewhere overnight when the children were present, but spending days with them in the home, and still considered it her residence, as she lived there full time when the children weren't present.
Mom lost custody for continuing to cohabitate against a court order.