Well the warrant doesn't matter, one he gave verbal conesent to search which he could have revoked at any time, so shame on you for not being aware of your rights. With the info they were given by "kenny" they did in fact have probable cause merely from the description, kennys statements and the prescenece of the f150 and trailer didn't help since it corrobarates kennys story even if its bullshit it makes it more truthful seeming to most people.
The whole story sounds fishy to me, I don't know you or kenny but it sounds like someone is lying or maybe both of you are lying, there are 3 sides to any story, one persons story, the other person story and then the truth. Not saying you did anything but then again you could have. Good luck with everything assuming you are innocent however you really should know your rights better than you do
but like I said they'd have gotten a warrant in less than an hour or 2 and the whole time one of those "pigs" would have been hanging with ya keeping you from destroying evidence or leaving. Using a slang term to describe an officer of the law doesn't help your case, it kinda makes me think you're hiding something by your ignorant attempt at humor or maybe its a verbalization of your hate of people who keep others on an even keel.
The fact is, if you reported your baby stolen you'd want those "pigs" working just as hard to find it or who took it if not harder.