Electric vehicles (EVs) link mobility and electric power availability, posing a risk of making transportation unavailable during blackouts. We develop a computational framework to quantify the impact of EVs on mobility and access to services and find that existing access issues are exacerbated by EVs. Our results demonstrate that larger batteries reduce mobility constraints but their effectiveness is dependent on the geographic distribution of services and households. We explore the trade-offs between mobility and quality-of-life improvements presented by Vehicle-to-Grid technologies and the feasibility and trade-offs of public charging infrastructure as a solution to access inequalities. Equitable access to essential services (e.g. supermarkets, schools, parks, etc.) is the most important aspect of community resilience and our results show vehicle electrification can hinder access to essential services unless properly incorporated into policy and city-scale decision-making.