Not being funny but HOW could she leave it there for 2 days; let alone 2 YEARS!! OMFG!!
DO THIS TOMORROW!!!:
You, your sister & 2 other friends / relatives / neighbours should wear old clothes; wellies; & rubber gloves...
Put a big heavy duty sack over the barrel & fix the sack with duct tape.
Then put the barrel on its side & cover it from the other end with a 2nd heavy duty sack; also taped.
Continue until there are enough sacks for you to not feel totally grossed out by the barrel eg. 6 sacks taped to the barrel (3 covering each end).
Use her or your car / or borrow another person & their car; put the back seats down; cover the boot & flat seats in old sheets or plastic.
Get a strong & shallow wood or plastic crate / box with very low sides, no lid & handles.
Make sure it is big enough to hold the barrel (once the barrel is lying on its side). (Basically check by using A Tape Measure to measure the height & width of the barrel...)
Roll the barrel to the edge of a kerb (eg) & bump it into the box.
Get an extra couple of people also with gloves; lift the crate containing the barrel into back of the car - secure it with rope.
(First measure the barrel-on-its-side-in-the-low-sided-crate to check it will fit into the car!)
2 of you get into the car with an Odour Neutralising Air Freshener for those stinky moments; the other 2 people follow in another car / taxi.
Drive to the local dump; produce a utility bill with sister's address; then lift the crate into the dump.
Drive home; clean out the car with diluted bleach (even though no poo will have touched the car - it will still make the car owner feel happier).
Bleach the area where the barrel lived.
Throw away gloves; wipe wellies & chuck old clothes in the wash.
Relax. No more poo barrel.
Make everyone some tea / pour out wine or whatever & wonder why the hell it took 2 years to do that.