Firstly two fingers is a subjective measurement. Two large man fingers is quite a bit more space than two petite women fingers (No sexism intended!).
If the dog is able to slip the collar between his teeth, it's a sign the collar is too loose. While it is vital to not have a collar too tight, a loose collar can also be a hazard and can be effective as a noose for adventurous pets.
Try putting the collar (a new collar!) on a bit tighter. If you are a man, use one finger gap, or even a pinky finger gap, as it is difficult to give a guideline without seeing the dog. A chihuahua-yorkie cross should have a reasonably thick head, as opposed to a slimline greyhound, or whippet, so there should be enough differential between the neck diameter and head to secure a collar without the dog getting it between his teeth.
The collar needs to be tight enough that it cannot be chewed by the pet and loose enough that the pet can freely swallow and the collar will not dig into the skin. When dealing with such a tiny dog, it is not always viable to go by two fingers, as the two fingers can be half the width of the dog's neck.
If you are having a problem finding a small enough collar, try using a cat collar. They can work well for smaller dogs.
If the dog cannot pull the collar off he will eventually adapt to it.
If she seems bothered by a fitted collar, you can try putting it on her for an hour a day and increase the time. Try to distract her with interactive play and treats while she is wearing the collar. You don't want to teach her that when she struggles you take the collar off, you are the master not the puppet so to speak.
Giving her a reward when you put the collar on and lots of verbal praise, and a play session can turn the collar into something that she can be excited to see, over time she will eventually forget that she is wearing it. I personally like to take my dog's collars off when they are in the home, to give their necks that freedom and stop any unnecessary hair loss, from rubbing that can happen with some dogs. This is a safety decision, as a collar is also an asset to have if a dog can escape from a yard, so this is not a blanket recommendation.
The best way to train dogs to become used to collars and leads is to put them on as young puppies and let them run around with them, make them fun, but your dog is past this small puppy stage.