The information is not easy to get but this government website states that you can claim attendance allowance and your wife can claim carer's allowance. One doesn't cancel out the other.
https://www.gov.uk/attendance-allowance/overview
However, for your wife to be claiming carer's allowance you must be in receipt of DLA, PIP or Attendance Allowance. You cannot get Attendance Allowance and DLA or PIP.
You get PIP if you are under 65 when you first claim for your disability or ill health (it used be called Disability Living Allowance and some long term claimants still get this). If you are over 65 when you first claim you get Attendance Allowance.