Super reward toys for training turn my minpin into a whining mess. What to do?

Jezebelle is a wonderful little girl, almost 2 1/2 year old MinPin that we've had since she was  9 weeks old. There are no training facilities around here, so I have trained her myself with the help of books and reading here and there on the internet. She's smart, almost too smart for her own good sometimes, but she is also willful when it comes to obeying commands. So, on that hand, we started her on NILIF when she was very young (thank God for this board!).  She knows sit, down, stand, spin, off, leave it, drop it, upstairs, etc.

I learned real early that she is overly excited if you use food as a reward, and her everyday toys aren't rewarding enough for training.  The only time I use food as a reward is when it is a command that uses hands on for demonstarting what you want, i.e. spin.  Forget food if you want to teach fetch, she forgets the toy and stares at nothing but your hands etc hunting for the food. She also has a very short attention span, so training sessions of about 5 minutes max. AND, she is very prey driven. So much so, that you can't even say the word 'squirrel' around her without her having a fit trying to find one.  She loves to hunt for lizards on the porch, but she will leave them alone when I tell her to (but not squirrels or rabbits). I've stopped opening the blinds so she can see outside, and removed the bird feeders that brought in the squirrels. I wanted to get her 'stay' and 'come' down without the constant distractions.  Well, so far, both are about 50% I would say. She is just so "I've got to see what's out there, you've got, he's got, etc. Like I said - very prey driven. And, she doesn't care for the clicker, so forget that method.

So, with some of the things I have read, I got two really special toys for rewards when training.  One is a mouse w/ squeaker (she loves squeaky toys) made of real rabbit fur, and the other is a small cloth covered squeaker like the kind used in the show ring as an attention getter. She LOVES both of them. Instant attention, and she is doing great on learning heel, come, and bring with them. BUT, when I give them to her as a reward for doing it right, she starts whining and whimpering and tries to find a place to hide it. She will give it to me with no fuss, but her whole body posture slumps, tail down, ears back etc.  The only other toy that she does that with is her hide a squirrel. She doesn't get that one except under supervision, and she'll play with it enthusiastically for a bit, then she starts whimpering and carrying them around. I have to take it away from her to make her stop. And she has the same reaction with her new 'rewards'.  The more I work with her with them, the quicker her slumping body posture and whimpering starts. I am at a loss at why this is, or what to do with her as a motivational reward.  It is apparent they encourage her to learn, but the training session isn't fun for her - or me. I can't get her too excited or she just gets 'deaf' during the session.

Any thoughts on her reaction to her reward toys? Or what to do to change her response? If it can be changed?  As much as I would love to take her to a training class, the closest one is over an hour away, and it is at one of the Pet***** stores.  The added distractions of that type of atmosphere wouldn't be good for her anyway.  We got her ILP last weekend in Houston, and I hope to have her starting her Novice Obedience by next April.  Any thoughts/help would be appreciated. Thanks!