So just to clarify, you want to ignore the £557 DLA she gets for having a disabled child whilst deducting an average amount given by a charity because she has a disabled child...
Or we could look at the actuals. Using your £2768, and the £557, she gets £3325. (Actually £100 more than the calculator suggests, but let's use the highest amount of rent too at £1000). So once you deduct the £1000 rent which she hasn't earned anything to cover, she has £2325 a month after housing costs. £536 a week to live on.
I think a lot of people, including those with disabled children would like £536 a week to live on, no work required. That £536 grosses up to £27900 a year. That's the equivalent of a salary of £34500. With no rent or mortgage.
To make it more comparable, you add back the rent, most people pay rent or a mortgage. £3325 take home. That's an equivalent salary of £51,900 a year. Do you think most people would be able to cope on £51,900 with £1000 a month rent to pay. I think most people would be delighted at that. Especially if they didn't actually have to work to receive that net amount in their bank. Many parents of disabled children have to work.
And it's looking at this £536 a week with no rent or mortgage that OP needs to ask, "why can't I afford to live?"