The separation logic of relations (SLR) is a generalization of separation logic (SL) which is useful to describe complex structures like graphs and relational databases. SLR extends SL by interpreting heaps as (multi)sets of relational atoms instead of partial functions. This paper addresses the satisfiability problem for SLR formulas with additional shape constraints (called patterns) expressing conditions such as uniqueness of atoms or functionality of relations. We show that the satisfiability problem is \(\textsf {2}\hbox {-}\textsf {EXPTIME} \) -complete when (dis)equalities over existential variables are excluded from the considered patterns, and undecidable otherwise.