score:2
You have misunderstood the requirements for a visit visa sponsor. It generally does not mean undertaking any legal responsibility, in the context of a standard visit visa it merely means that a 3rd party(ies) is providing funds, maintenance and accommodation per V4.2 if the Immigration Rules https://www.gov.uk/guidance/immigration-rules/immigration-rules-appendix-v-visitor-rules You do not have to be a UK resident to sponsor a visit visa application.
IMHO you are over-thinking this. In your shoes, I would get invitation letters from both your parents (the dates should tally with the dates in your application, although this does not mean you canβt change them once the visa is approved), write a cover letter to explain anything thatβs not already covered in the application What details should a good cover letter contain to back up a UK Visit Visa application? and provide the relevant financial information relating to yourself (copy passport, bank statements, employment contract etc). https://www.gov.uk/government/publications/visitor-visa-guide-to-supporting-documents/guide-to-supporting-documents-visiting-the-uk Thereβs no need for your parents to send mortgage documentation.
Finally, you mention that you both have ample savings to cover the trip. If your wife can demonstrate that she meets the eligibility criteria without the need for your sponsorship, she could apply with just the invitation letters and her own supporting evidence.