Initiatives to integrate technology in schools are continuously increasing, with efforts to bridge the "homework gap" and provide technology access in low-income households. However, it is critical to include nondominant parents in technology adoption decisions in order to avoid mirroring past patterns of inequality in home-school relationships. This study examines the digital access, use, and beliefs of Spanish-dominant immigrant parents, whose children attended a school in early stages of 1:1 (one laptop, one child) and BYOD (bring-your-own-device) initiatives. Informed by critical and ecological approaches to family literacy and technology use, the analysis compares the cases of eight parents attending technology workshops facilitated by the researcher and looks at the factors and contexts shaping their digital access and use and their shifts in access over two years. The analysis then narrows down to their beliefs about the use of school-provided devices. Findings illustrate the diversity in device use and customization in families with similar immigration trajectories, showing how economic factors, education, and established livelihoods in the community shaped their decisions to obtain devices and Internet connectivity. Cases also show the crucial role of the school in providing computers and technology training; however, decisions about taking school devices home and supervising children's activity were shaped by parents' beliefs about their roles supporting their children's moral education, and their existing family practices. Implications for family literacy programs and outreach for digital equity in new migration settings are discussed.