Ok -- first off, calm down (I'm not scolding -- but you're upset, he's upset, and it all changes the 'air' and a dog can SMELL that).
Realize he's had a lot of trauma in his young life, and likely separation anxiety was what got him bounced to begin with. Shame on that rescue for not knowing this and letting you know.
HOWEVER -- You absolutely must take this slow, and it's already gotten off on a bad foot.
Crate-training has to happen in small increments -- and it has to happen while you build confidence. he's probably terrified that he's going to be left again, Beagles are kind of pack animals to the upper degree -- and crating him in a room AWAY from the other one is not not not not not gonna happen.
Get TWO crates -- put them side by side (and I tend to like a wire crate so they can literally feel like they are in the same 'den', hear heartbeats, etc.). Then you crate train both at the SAME time. You feed in there, give treats in there, all while leaving the door OPEN. This has to go in super super SMALL tiny increments.
I can hear you "We don't have that luxury -- we both have to go to work TOMOROW"
You have a decision to make -- you will have to make some changes and keep them together (probably in a small, prepared room) and maybe even take BOTH to doggie day care at least Monday, and maybe at least the newbie all week while you crate train AT HOME, and work on this intensely over the next week or so ...
OR -- take him back to the rescue and let them re-home him.
But honestly you can make this work if you work on it hard and make some concessions.
It will mean changes for both dogs -- there is nothing cruel about crating the established dog next to the newbie -- they'll keep each other company, and altho it will be a change, it's not a bad thing at all.
We humans get this thing about thinking they have to 'be free'. They don't. Dogs are den animals. Some do fine loose in the house, some don't. It is just too much worry and too much 'stimulation' for many. But -- to the end of helping the newbie get established and everbuddy being happy, you can do it.
But -- you don't really 'leave' them at first. You don't even shut the door at first. Particularly since he's probably got a major crate-anxiety going as well. You simply make ALL GOOD THINGS happen in that crate. Food. treats. Even company. Putting them in the crates, and then either sitting there with a book or magazine or watching TV -- so you are 'there' while they are in the crate. No big deal.
Gradually you shut the door while you ARE there. Never open the door when there is whining. Use the established dog's pre-disposition to be 'ok' with stuff while you are there to praise as an example to the newbie.
Your first 'leaving' should be something like "Guys I gotta get something from the kitchen -- I'll be right back. shh now."
You get up, you dash out into the hall and RACE BACK IN before any barking starts. You gotta set them up to succeed here. that means you have to orchestrate success sometimes - so you can 'reward' something before trouble begins. "Wow, what'd I do right?" You really want to leave them with the idea that they did NOTHING and got praised.
Because frankly -- that's exactly what you WANT. *nothing*!!!!
I realize that doggie daycare extra days may be way more than you wanted to spend -- ask them .. maybe they'll cut you a deal or let you stretch out payments. If you are good customers they should work with you -- particularly in the interests of helping establish a new dog.
But above all -- please try and be calm -- this little guy has had a TON of changes just this weekend. He's got baggage -- most dogs do. He got scared and then YOU got upset and ... that made him MORE scared. And when humans get scared they give you away!!!!
Make sense?? Good luck.