OP,
I completely agree with poppy, you have to base your appeal on you the PIP activities / descriptors. This is how a tribunal panel will arrive at a decision. (Don't expect the DWP to overturn their decision at MR stage).
https://www.benefitsandwork.co.uk/personal-independence-payment-pip/pip-points-system
The link poppy has supplied to the assessors guide will be very helpful. Look carefully at the reliability section.
This is a good guide to the appeal process:
https://www.advicenow.org.uk/guides/how-win-pip-appeal
If you follow this guide, and keep in mind timescales, it should help you through the process.
At the hearing, your wife's verbal evidence will be very important.
I would echo poppy's remarks about not being too angry about the report. Point out any internal contradictions in it, but in your written statement explain how and why the descriptors apply. Your wife can explain further at the hearing, and give examples / illustrations of these activities to the panel from a typical week / month.
If you can get help from your local advice agency / CAB, then I would suggest you do so.
https://www.citizensadvice.org.uk/benefits/sick-or-disabled-people-and-carers/pip/appeals/mandatory-reconsideration/
Was this a renewal? Was your wife previously in receipt of PIP?
If so, then there is some case law around the DWP having to give very precise reasons for ending a claim on reassessment (particular for chronic, degenerative, and continuing conditions).
Alice Holt Forest situated some 4 miles south of Farnham forms the most northerly gateway to the South Downs National Park.