Slimey poo means it's mucous which is a sign that something is going on- could be anything from worms to a virus, like mom2many said. Usually mucous in the poop (from what I remember) is the sloughing off of the intestinal lining due to an overgrowth. In Daisy's case it was yeast, but it could be caused by a bacteria or intestinal worms. Do you have them on a heartworm medicine (that can prevent both heartworms and intestinal worms)
I would be nervous because all three of them are having the same thing- could be something that's going around your house. It definitely could be from the snow- you don't know what was on it when it was there- like if a stray dog pooed on it- and then your pups drank the water. I remember Laura C (with the border collies) a while ago all three of her dogs had a virus or bug, and a couple days later she got sick too.
I know you say that you don't have the money for a vet, but if you could maybe just take a stool sample from one of the dogs in (at my vet it's only about $20-$30), and if they find something, they will probably give you some medicine for all three- from what I've learned if one of them has something, all of them are going to get it. My vet knows my college financial situation, so she doesn't make me pay for an office visit.
As far as the destructive dog, I would get a crate for that one, and start crate training ASAP. Daisy started to get destructive like that when we moved into the house at school. She's learning to be good in the crate right now, and with some rescue remedy, she doesn't get as anxious in the crate as she did before.
"Until one has loved an animal, a part of one's soul remains unawakened" ~Anatole France