mslc
Welcome to the forum
I have deleted part of your post as it included your full name and email address.
To try and answer your question.
Whilst ESA is a single benefit it has two methods of qualification.
The first is based on the claimants National Insurance record. To qualify for Contribution Based ESA your wife needs to have sufficient NICs in the last two full Tax Years (2011-12 and 2012-13), if your wife has not worked for three years then it would be unlikely that she will meet this requirement.
You can also get Income Related ESA which is subject to a means test of household income, assets and savings and (for completeness) any hours that you work. See
Asset rule for ESA(IR) 24 hour work rule for ESA(IR) If she ticked the box for an ESA(CB) claim only then the DWP will not have checked whether she was also eligible for ESA(IR).
If she did not tick the box then this may mean that either you have too much saved or some form of income (a pension?) that is preventing the claim.
If you need any additional information, please reply to this post and we will do our best to help.
Gordon