Extreeme Hardship is a legal term in the Unites States of America's Immigration Law.
Note that the hardship to the defendant is not relevant here, only the hardship caused to the qualifying family by removing the defendant or excluding him from admission. The wavers are govenred by INA 212 and INA 237 (potentially some others: add?). The United States Waiver of Inadmissibility application is required for INA 212 wavers, while INA 237 wavers do not have such application.
Here is a quote from BIA (Board of Immigration Appeals) rejecting appeal of a waver:
"U.S. court decisions have repeatedly held that the common results of deportation or exclusion are insufficient to prove extreme hardship. See Hassan v. INS, 927 F.2d 465, 468 (9th Cir. 1991). For example, Matter of Pilch, 21 I&N Dec. 627 (BIA 1996), held that emotional hardship caused by severing family and community ties is a common result of deportation and does not constitute extreme hardship. In addition, Perez v. INS, 96 F.3d 390 (9th Cir. 1996), held that the common results of deportation are insufficient to prove extreme hardship and defined extreme hardship as hardship that was unusual or beyond that which would normally be expected upon deportation. Hassan v. INS, supra, held further that the uprooting of family and separation from friends does not necessarily amount to extreme hardship but rather represents the type of inconvenience and hardship experienced by the families of most aliens being deported. The AAO recognizes that the applicant's spouse and/or children would likely endure hardship as a result of separation from the applicant.
However, their situation, if they remain in the United States, is typical to individuals separated as a result of deportation or exclusion and does not rise to the level of extreme hardship.
In case of INS 212(i) or 237 (other?):
Additionally, in case of 212(h) wavers
The hardship caused to children is not considered at all for certain types of wavers due to the presumption that "merely breading on US soil does not allow one any claims to US citizenship".