[Ladylavender]

If your puppy is pooing and peeing in the crate, then the crate is too big. (it may be the smallest crate they make, but it's still too big for a 2-3 lbs puppy. You need to make the crate smaller by stuffing cardboard, boxes, towels or things in the back so that all there is left is about 1/4 of the floor space available. (as she gets older and bigger, you can start making more floor space in the crate to accommodate the growth, but it should still only be large enough to stand, turn and lay down.) You should be able to keep her in the crate now for longer periods of time to begin to train her to "hold" her pee and poo for several hours. BUT you must work up slowly to more hours.

I would also get an x-pen and make this the "designated" potty area. I would set up the x-pen (out of the way, but easily accessible.) I would put down peepads to cover the floor of the x-pen area. (This will give your puppy plenty of room to sniff to pee and allow her to run back and forth to stimulate her to go poop) I also would suggest putting her scent on a clean peepad to start things and also put some smeared poo in there too. (not a lot) Dogs need to smell poo to stimulate them to go. I would bring her to this area on her potty schedule. I would make her walk in the x-pen herself (treat her to walk in) and then I would close the gate and let her do her thing sniffing and walking around until she goes. Treat and praise the potty. (repeat the "go potty" phrase while she is in there before and while she goes. By giving her an enclosed area to go and a bigger space to go, you are giving her a better chance to succeed. Also she will soon learn she gets out of "jail" after she goes potty and she can play. If she decides to play or she gets distracted, redirect her and keep repeating "go potty". After a time, she will go on command and you will be able to make her area smaller and smaller, by removing peepads and making the x-pen area smaller, until eventually she is down to one pee pad, but this could take months. Just be consistent.

Unfortunately, waking up in the middle of night is unavoidable, unless you do as another poster said and to set up the x-pen with her bed, toys and peepads. I don't recommend this, because you want to separate her potty area from her sleep area. You essentially want to train her to differentiate between her "den" and the "soil" area. If you combine the two, then she will also think it's ok to soil in the "den". Eventually her "den" gets bigger and bigger as she has access to other areas of the house when she becomes more reliably housebroken and she has to understand that these areas are NOT "soil" areas. That there is only ONE soil area and that's the area you have established from the very beginning and it never changes.