Recently, unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) is emerging as a promising technique for achieving robust and rapid emergency response capabilities. Such a novel framework offers high-quality and cost-efficient C\&S services due to the intrinsic flexibility and mobility of UAVs. In parallel, rate-splitting multiple access (RSMA) is able to achieve a tailor-made communication by splitting the messages into private and common parts with adjustable rates, making it suitable for on-demand data transmission in disaster scenarios. In this paper, we propose a coordinated RSMA for integrated sensing and communication (CoRSMA-ISAC) scheme in emergency UAV system to facilitate search and rescue operations, where a number of ISAC UAVs simultaneously communicate with multiple communication survivors (CSs) and detect a potentially trapped survivor (TS) in a coordinated manner. Towards this end, an optimization problem is formulated to maximize the weighted sum rate (WSR) of the system, subject to the sensing signal-to-noise ratio (SNR) requirement. In order to solve the formulated non-convex problem, we first decompose it into three subproblems, i.e., UAV-CS association, UAV deployment, as well as beamforming optimization and rate allocation. Subsequently, we introduce an iterative optimization approach leveraging K-Means, successive convex approximation (SCA), and semi-definite relaxation (SDR) algorithms to reframe the subproblems into a more tractable form and efficiently solve them. Simulation results demonstrate that the proposed CoRSMA-ISAC scheme is superior to conventional space division multiple access (SDMA), non-orthogonal multiple access (NOMA), and orthogonal multiple access (OMA) in terms of both communication and sensing performance.