In this paper we explore cooperative manipulation of a flexible structure using a team of two nonholonomically-constrained, differentially-driven robots. Cooperative manipulation is achieved by tracking relative trajectories that are designed for both the nonholonomic nature of the platforms and path constraints limiting the deformation of the flexible structure. The relative trajectories are designed by transforming an optimal-trajectory problem to a nonlinear programming problem. A tracking control law is also designed for the nonholonomic nature of the platforms with consideration for the challenges in cooperative manipulation. Results are presented for a simulation example, and a hardware demonstration for a simple case is used to demonstrate the feasibility of the approach.