Quote: He cries all the time if I'm sitting in front of him... He wants me to pick him up. (Like a baby) I don't hold him a lot at all I think it became this way because I've been leaving him behind to go run errands.
I honestly don't think it's a matter of him being clingy. He IS a baby, and all he wants is your attention/affection. I hunt my Beagles and I can tell you they are happiest when in a pack situation, in the middle of other dogs and humans. Even when retired, my old huntin' dawgs (lol) will get this way. If they can't be part of the dog pack, they want nothing more than to be with their humans. Even when I raise a litter, I find that despite having half a dozen other pups to play with, each one is drawn to seek attention from me & the other people in my household. "Tapping" the owner to be held is a VERY beaglish thing. They are not an independant, aloof breed in the least.
I view this as constantly refusing to hold a baby when it cries. Pups need tactile stimulation just as much as a human child & if you deny them that, they will start to become less trusting of humans and unsocialized.
Picking up a puppy and showing it affection is not spoiling the animal.
As far as the soiling the crate goes, puppies do need to move their bowels and urinate more frequently than adult dogs. Pups under 3 months should not be expected to hold it for more than 2ish hours. If he was a pet store puppy or raised on wire by the breeder, a crate will likely not work as a housebreaking tool. What about leaving him in an ex pen with some wee wee pads in lieu of the crate when you're not there to supervise him?
Puppies are a great deal of work, especially Beagle pups. Regardless of age, he needs more exercize than he's getting, and more one on one attention. You mention you're leaving on errands, then when you return, you're not giving him the simplest form of attention that this pup is craving. It doesn't matter how long you're gone, what matters is that when you return you need to spend time giving him quality attention - or what is the point of having a pet puppy? I'm very sorry if I sound harsh, but in all your posts about this pup, you come across as resentful of him, his normal puppy accidents, normal puppy behavior, and even something as simple as him wanting a bit of love and attention from you. Please be honest with yourself, and if this is not the right time for a pup to be in your life, do the right thing by him and find him a home with a family who has the time for him.