Cute baby! There is a lot of information about potty training, crate training, and timelines for puppies if you use the search bar! I've scoured the posts for my first puppy and there is so much helpful information accumulated on these boards.
First and foremost since the allergies prevent the puppy from being crated nearby, the most recommended method I've seen for the crying at night IS TO IGNORE IT! I know, it's exhausting to hear all night long, but she will settle down. Sometimes it takes a week, sometimes a few. Luna took a few weeks before she quit altogether. You really don't want to associate the crate to a bad scary place by having your husband intimidating her like that (which can be VERY scary to be intimidated by their humans for a 10 week old!), so I'd ask him to bear with it and if it's too much, perhaps look into ear plugs for the week or so it could take
Be sure to start associating the crate positively away from just being jailed for the night
Be sure to play games in the crate, leave treats throughout the day, use treats to lure your pup inside and also treat with the door closed! You want to teach her that the crate is a good place, a safe place for her.
Our game involves high value treats, something the pup LOVES but ONLY gets associated with the crate. We lead them in, praise! Give the treat. Over time, we then show the treat and throw it in the crate, close enough to the door it can be smelled but far enough so the pup goes inside to get it. Close the door, wait a minute or two, then let them out. It teaches them that it's not a "jail" and good things happen in the crate with and without the door open! Feeding in the crate helps associate a personal place as well.
You could try leaving on soft music at night for her, or look into the "heartbeat" cuddle buddy toys to try to keep her calm while in the crate. Just be sure not to take her out while she's crying, it teaches them crying = get what I want!
As for training, I wouldn't force her into anything that's obviously making her uncomfortable and afraid. Slowly introducing her to new situations to build her confidence is much better than just throwing her in to swim, so to speak. Too much stimulation for my puppy (Luna) was a bad thing since she was a skittish/nervous puppy. So go at it based on your sense of how she's doing or what she can handle. Learning to walk on a lead, do walks, or venturing far from home takes much more time (months even) to train and build their confidence and build your bond together. The "stop and become a tree" method is good at helping redirect them from over taking you on the leash, but be sure to reward or praise graciously when they do come back to you since that's the point! You want to show her YES! this is what you're supposed to do! good girl!! Learning to walk with the leash/offleash in the yard and short distances helps a lot too by doing those exercises with treats and praise and short distances.
At the end of the day, she's only 10 weeks old! She's still SUCH a baby and just left her litter not long ago. Take it slow, training doesn't need to happen immediately. It's great to create a bond with her with fun training as a puppy, but you really want to focus on positive play/train and bonding together. Again congratulations on your new puppy!
All the information from me is just what I've gathered from my research in the forum first with Luna and now with our 2nd pup. Others will have much more experienced advice/experiences of course. Best of luck!