Agree. I think, though, that he had TWO back up plans, both that blew up literally in his face.
He had these papers, just in case Kelsey "disappeared" on her own, so to speak.
He wanted Krystal to do the dirty deed and be the suspect. Think about it- it wouldn't be hard, if she had committed the murder instead of him, to believe another woman wanted to get rid of the woman preventing them from being together.
When Krystal refused two or three times to kill Kelsey (sorry, but I do think that coffee was poisoned and agree with
@ilovechili that that is a woman's way of murdering someone-less messy), he had no choice but to do it himself. He thought he was so smart, making her clean up the mess, helping him burn and dispose of Kelsey and evidence. He thought he was free and clear, and eventually, had he gotten away with it, I think he would have told Krystal to take a hike. I think the custody papers were the back up plan to file, once Kelsey "disappeared". Patrick even mentioned some co-worker of hers, a male, tried to insinuate something was going on between them, to question him.
Patrick thought this out carefully, in terms of how's, when, back up plans. He didn't think out the evidence trail- though he thought he did, having him and Kelsey text back and forth after he killed her, and then Krystal bringing Kelsey's phone back with her, making it appear that she either went to visit her ailing grandmother (I wonder if that was a lie, too, or was Kelsey's grandmother ill and he took advantage of that to create a false story?).