Which out of the two has greater bond angle? Water or diethylether.Why?
You are mostly correct with your reasoning , and the $\ce{C-O-C}$ bond angle was indeed expected to be lesser than that of $\ce{H-O-H}$ bond angle of water . But it's all theoretical. Experimentally the opposite was observed and was explained on the basis of steric hindrance or steric repulsion of the two bulky $\ce{C2H5}$ groups.

In case of $\ce{(C2H5)2O}$, the positive deviation of the bond angle can be explained on the basis of steric crowding of two ethyl groups. They repel each other and as a result , they do not let the lone pairs of Oxygen compress the bond angle more . 

$\ce{H-O-H}$ bond angle is found to be $104.5^\circ$ whereas the $\ce{C-O-C}$ bond angle in diethyl ether is found to be roughly close to $110.5^\circ$. It can be attributed to the steric repulsion that trumps the bond pair-bond pair and lone pair-lone pair repulsion in this case.