Ask an Immigration Lawyer. Get an Answer ASAP.
The concern may well be that as the parents of a US citizen they are immediate relatives and could apply for greencards. The consulate may be concerned that they would enter as visitors and then stay to apply for their greencards from within the US instead of through the consulate.
If your family owns their home in Peru, or has a business or employment that they would need to return to, that would be important to show to the consulate. Also, if they have younger children still in their care, or if they have other grandchildren in Peru that they care for, that would be another substantial reason to show that they would return to Peru after the visit.
The 38,000 is likely sufficient - they are not looking to see if you are wealthy, only that your parents would not need to engage in unauthorized employment during their visit to support themselves.
Would your parents have any of the above items to show to the consulate?
Oh - ok. That your wife is not yet a citizen should lessen the concern that they may apply for a greencard while they are in the US as visitors. They should bring in proof of everything they can, but, unfortunately, the grant of a visitor visa is descretionary and can be denied for fairly arbitrary reasons. The more they can show in terms of home country ties the better. I would not focus on their age unless they are about to or do qualify for benefits if they remain in Peru that they would not otherwise qualify for - anything to show that it is in their own self interest to return to Peru and not overstay a visitor visa.
You may also want to be clear that they would not be intended as babysitters while here - just meeting the grandchildren.
I wish I could tell you more to help with this. The only other alternative to a denied visitor visa is to look to other options - such as your wife naturalizing and filing for their greencards. Obviously there is an irony there - that in doing so she could get them in to the country, but that would require their showing an ability and desire to remain in the US, rather than the desire and reason to return to Peru required by the visitor visa.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).