ACh contracts the wall of the bladder(by M3 receptor). How does it relax the sphincter?
According to this paper (full text freely available), "the somatic pudendal nerve stimulates striated muscle of the external urethral sphincter, mediated by ACh activating nicotinic (N) receptors" (from Figure 2 caption).
On page 83 of the paper the Guarding Reflex - which is the bladder-to-external urethral sphincter (EUS) reflex - is explained, and in the top-right it says:
In order for the guarding reflex to be reversed and the EUS relaxed, a final inhibitory signal is generated from the pontine micturition center (PMC). Bladder afferent fibers in the pelvic nerve form synapses in the spinal cord, and axons from the second-order neurons travel rostrally to the micturition center. The center integrates this sensory information with signals from more rostral brain regions and ultimately generates inhibitory input to the sympathetic and somatic centers in the spinal cord and stimulatory input to the parasympathetic center (Fig. 5). This spino-bulbo-spinal reflex results in relaxation of the EUS and internal urethral sphincter, followed by contraction of detrusor muscles, increase in bladder pressure, and flow of urine .