A relative of the youngsters, Sheena Paterson, 48, wept in court as she was led away to start her sentence yesterday.
Sheriff Derrick McIntyre told her: "The abuse has had a traumatic affect on these young children and goodness knows what long-term psychological damage may have been done to them.
You are a first offender but such is the nature of this offence it is only appropriate that a custodial sentence be imposed."
At an earlier hearing at Edinburgh Sheriff Court, fiscal depute Melanie Ward said the incidents had a "traumatic affect" on the two children, who were aged four and six when the abuse started.
Ms Ward said concerns had been raised and the children were interviewed by authorities.
She said: "It transpired both children had been placed in the bath whilst clothed and their heads were held under water."
Paterson, of Oxgangs Farm Drive, Edinburgh, admitted attacking the children between March 29, 2004, and May 28, 2007, at an address in the city.
Defence agent Stephen Knowles appealed to Sheriff McIntyre to place her on probation. Sheriff McIntyre said he had reduced Paterson's sentence from 18 months to reflect her early guilty plea. He ordered Paterson to be on supervised release for seven months after her jail sentence.