It is possible to condition extremely positive emotion towards the crate, and still have them sleep in the bed at night. Unless... Are they peeing in the bed at night? Or are you such a light sleeper you won't wake up if they do?
If crating is not an option, and you won't consider it at all, then maybe tethering to you and lots of leashed walks to a potty spot (pop out the door, pop back in) is your next best bet. And when I say lots, I mean LOTS... Like every hour at first, every 2 hours, then 3, and so on.
You'll have to either invest the time in conditioning the dogs to a crate (a clicker, some treats, and patience...) or you'll invest the time in taking them out a lot. Either is fine, really, depending what you prefer. If you don't mind running dogs out a lot, and not being able to leave the house without them until they learn, then that works. If you've got a less flexible schedule, crating is likely to be most successful.
Good luck!