Litopenaeus vannamei stands out globally in aquaculture for its fast growth, broad salt tolerance, disease resistance, and high protein levels. Selective breeding requires the precise estimation of the variance components and genetic parameters for important traits. This study formed lineages from 20 full sibling families of L. vannamei, with progenitors from Thailand and the USA. We then assessed the genetic resilience traits of juvenile shrimp from these families to high ammonia-N, high pH, and low salinity by performing a 96 h acute toxicity test. Mortality rates for the families under 96 h exposure to high ammonia-N, high pH, and low salinity were 19.52–92.22%, 23.33–92.22%, and 19.33–80.00%, respectively, showing significant variance in stress tolerance among families (p < 0.05). Survival heritability estimates, using threshold male and female models, were 0.44 ± 0.12 in high ammonia-N, 0.41 ± 0.12 in high pH, and 0.27 ± 0.08 in low salinity, respectively. Genetic correlations between growth and stress resistance traits varied from 0.0137 ± 0.2406 to 0.8327 ± 0.0781, and phenotypic correlations ranged from 0.0019 ± 0.0590 to 0.6959 ± 0.0107, indicating a low-to-high positive correlation significant at (p < 0.05). It was found that the survival rate of families No. 2 and No. 9 was higher under high ammonia-N and high pH stresses, while the survival rate of family No. 10 was higher under low salinity stress after comparing two selection criteria, the breeding values and phenotypic values. Thus, these three families are identified as potential breeding program candidates. Through the creation of a genetic parameter estimation model, the genetic variances across mating combinations for stress resistance traits were obtained and families with heightened stress resistance were identified, laying the groundwork for enhanced genetic selection of L. vannamei.