It is really completely simple. If the annuity is in your name - i.e. the income is yours from an annuity you bought or took out as a result of pension contributions you made - then it is your income & has to be taken into account as such for any means tested benefits.
What you do with the income (i.e. in this case you say it goes to your children) does not alter the fact that it is your income, & the use which you put it is irrelevant so far as any means tested benefit entitlement is concerned.
Do not bother to appeal this - you will be wasting your time.