If my 21 year old works while living with me, will this effect my ESA and PIP or housing benefit?

Oh i see. This tells me that she doesn't receive the carers element of UC either. All she's claiming is the standard allowance for under 25's. In an earlier comment you said she claims carers allowance which is UC, this is not correct.

This means that the work that she's planning on doing will reduced her UC to zero and her claim will close.