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.
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