Your petition for her is in the F4 category (sibling of US citizen), which has a wait for visa numbers of almost 13 years for most countries. If one of your parents petitions her, that will be in the F2A category (unmarried under-21 child of permanent resident), which has a wait of 1-2 years, but might age out into the F2B category (unmarried over-21 child of permanent resident), which has a wait of almost 7 years, before her priority date becomes current. You can check each month's
visa bulletin for what priority date is current in each category. From the birth date you gave, your sister is 19, not yet 20. She has a little more than a year to go until she turns 21, and under the CSPA (Child Status Protection Act) the time it takes for the petition to be approved can be subtracted from her age, so depending on how long the petition takes to approve (which is not under your control), and how the priority dates move, it's possible for her to be barely able to immigrate under F2A.
Since the category is not current, she cannot file I-485 (Adjustment of Status) or do Consular Processing until the petition is approved AND a visa number is available for the priority date. (The petition will be approved well before a visa number is available, so the controlling factor is when a visa number is available.)
Multiple people can petition her at the same time; they do not conflict. Either parent can petition her. When your parents enter the US with an immigrant visa, they immediately become permanent residents, and can file the petition on that day or any time later. Note that for your parent's petition to work, she must remain unmarried, as there is no category for married children of permanent residents.