I have two yr. Old lab and beagle mix, she use to love going out and now she hates it my 19yr. Old daughter tries to take her out but nothing she has not gone to the bathroom in two days yesterday I tried and it was a struggle but finally she did a little urine and that was it what should I do?

If she is not "bathrooming" she needs to see a Veterinarian to see if she's healthy.

After that - did something, anything, frighten her outside?

I know when my daughter was taking her out my daughter would come back and tell me she is afraid of noises and big dogs, now my dog thinks twice about putting on her collar and going out

Is this a sudden change in her behavior?

Her behavior was like this with the big dogs for a while but now her fear has gotten worse with everything like noises, winds, storms I have a feeling she has developed operations anxiety she is with my daughter all day, and my daughter loves her so much she is worried

I meant "seperation anxiety"

If she hasn't defecated in 48 hours you should really seek medical attention. If it is only behavioral I would highly suggest seeking a obedience trainer/behavior modification, as this will help her with self esteem and create a less anxious environment for her.