Family pensioner business in a partnership firm

There will not be any problem. She will be eligible for family pension even though she starts a business or she becomes a partner in any business. But the income she is getting as pension should also to be shown as her income and tax is to be paid on this amount also.
Nowhere it was stated that the pensioners can't work anywhere. Many of the retired employees are joining in other jobs and they are getting both the pension as well as salary from the present job.
One of my distant relatives was working in the government sector. His wife also was a government employee. When she died her husband started getting the family pension. He was already retired and he was getting his pension. So now he is getting two pensions. One is the pension he gets after retirement and the other is Family pension from his wife's pension after her death.

Pension is like a reward or royalty for the long service done. It does not restrict one to do some work.

Any income derived from business partnership or any other occupation is to be clubbed with pension and if the total income exceeds the Income Tax limit stipulated for tax then one has to pay the income tax and file the return accordingly.

Depending upon ones capacity and capability one can take up even multiple jobs. There is no restriction on that.