Hiya!
First off, please don't use your puppy's crate/kennel to punish her. I'm not lecturing or anything and I know it's difficult (my little Badger can drive me crazy sometimes!) but the kennel/crate is a recreation of the wolf den which is a deeply ingrained zone in all dogs irrespective of breed and size. The den is where they go to feel safe and comforted and it should be used for when you have to leave for a period of time, when you're too busy to focus on her and when you need to give her a time out for her naps or main sleeping. The kennel/crate should never, ever be used to punish her. If you want to reprimand her using the isolation method, then leave the room for about a minute. This is much more likely to get a desired response from her. Dogs are hard-wired to do two things: MAKE YOU HAPPY and BE A PACK ANIMAL. The standard response for any negative behaviour is always ignoring - no smacking or any other type of punishment (including tapping her on the nose)
You haven't said how long you've had her but I can tell you with certainty that the first month or so is a little difficult because they're getting to know you. I've had Badger now for five weeks and it's only been in the last week or so that he's finally 'getting to know' me and bonding. Up until then, he was very much following his litter mates' behaviour which includes lots of nipping and biting. You are doing 100% the right thing in saying 'no biting' to her in a firm voice. In my limited experience: it's all about tone and not what you say. Have a firm but gentle tone and keep your voice low. Dogs growl at each other and it's the lower end of the scale that gets their attention. You are her leader and the central pivot of her whole world. Big responsibility huh?!
As much as possible, don't let her put her mouth on you for any reason. Be very firm with this. It may seem like she's biting you out of irritation and what have you but in fact it's more than likely that she's either excited or a little scared and intimidated. You know you love her and wouldn't hurt her but she doesn't know that yet. Do what they do in the litter:
if she nips or bites, yell in a high pitched voice (don't scream or frighten her) and walk away. You may need to do this several times a play session but she will soon get the message, believe me. I didn't think it worked but a month down the line, Badger occasionally mouths but there's no pressure now at all and he's just learning but he knows straight away and tries to suppress it by putting his paws over his mouth or licking my hand. They are amazing animals! If it's just a little bite (like when she's excited or playing) then just stiffen your hand and say 'no biting' even in a slightly playful voice. Just keep reinforcing all the time and use a rough scale of response. Little bites, little response, bigger bites, big response. If she's particularly snitty, then gently flip her over on her back and tickle her tummy. This is what their mother's do when they're getting out of control and it works 100%. You then give her the message that you are in control. Leave her on her back for a few seconds and hold her there, even if she struggles all the while tickling her tummy and talking to her in a low and gentle voice. You should do this periodically with her every few days as part of your play or cuddle sessions. At first Badger hated me doing this but he loves having his tummy tickled anyway and we've turned it into a kind of game now. He now just lies there and licks his lips. He knows who's boss!
There are some other things you can do. When she's sleeping or relaxed on your lap, put your fingers in her mouth gently and rub her teeth. She may resist at first but be gentle with her and do it as much as she'll let you. In time, she'll have no problem at all. She must get used to people putting their hands in her mouth anyway. This is a good tip for cleaning their teeth too which should be done every day if possible. Also do the same with her ears - gently rub them and her paws and tail area. She should also be used to 'looming' hands over her so play games with her where you come up quietly behind her, say her name and then give her a treat. This way she'll learn not be frightened of being handled or hands coming from unexpected directions
In terms of the puppy classes, some here may disagree with me but I think you should ask for a refund. It sounds like an awful experience for both you and little pancake and as far as I'm concerned, it could have turned very nasty indeed. If they won't give you one, then do as someone else here suggested and give them some feedback, asking that your puppy be exposed to smaller more friendly dogs. I don't think off-leash classes work myself. I've had some bad socialisation experiences with my puppy so I've decided I'm going to ask my vet for some names of other people in the practice with small or similar breeds and arrange a meetup for us all in a park or something. Chances are there are other people out there with the same problems so maybe think about that as one solution. All in all, it doesn't sound like a good or safe operation to me frankly
I also think you sound like you're a lovely and gentle person so don't get too caught up with the 'right' and 'wrong' things to do. Alot of this is gut instinct I think, so follow your heart and do what you think is in both your and pancake's best interests. She sounds like a little sweetie and in time, with a little patience, you'll have a lovely little honey who'll never be happier than when she's made you happy. Let me know if there's any other tips or advice you need because it sounds like we're roughly at the same stages with our puppies and I could do with some advice too
. Annie x