If my dog bit my mother-in-law and she got a bacteria infection so she had to have her fingers and legs amputated, can she sue and collect for pain and suffering?

Your mother-in-law should file a personal injury claim with your insurance carrier.  When she completes her medical treatment and is either released by the doctor or is declared by the doctor to be permanent and stationary  which means having reached a point in her treatment where no further improvement is anticipated, her settlement with your insurance carrier should include compensation for the medical bills, compensation for pain and suffering, and compensation for wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for pain and suffering is an amount in addition to the medical bills based on the information in the medical reports.  Compensation for wage loss is straight reimbursement.

If the case is NOT settled with your insurance carrier, your mother-in-law can sue you for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable dog owner would have exercised under the same or similar circumstances to prevent foreseeable harm).  If this was the first incident of your dog biting, your mother-in-law's lawsuit against you will be for negligence.  If your dog has a history of biting, your mother-in-law's lawsuit will have separate causes of action (claims); one for negligence and a second cause of action for strict liability.  Strict liability is liability whether or not due care was exercised.

Your mother-in-law's damages (monetary compensation she is seeking in her lawsuit) will include compensation for the medical bills, pain and suffering, and wage loss as discussed above.  If the case is NOT settled with your insurance carrier, your mother-in-law must file her lawsuit prior to the expiration of the applicable statute of limitations or she will lose her rights forever in the matter.