As Dillydaydreamer says, as you are providing the care in your home, rather than the child's home you need to be registered as a Childminder (if in England, Wales or Scotland) as care is being provided after 2am. Childcare between 6pm and 2am is unregulated, but care between 2am and 6pm is regulated - see Childcare Act 2006.
There is some call for Respite care. However funding for such care can be tricky to get from Social Service departments, which leaves parents having to fund it themselves which can be very costly. Social Services may help parents fund such care via Direct Payments.