  In this paper, we study a collection of mean-reflected backward stochastic
differential equations driven by $G$-Brownian motions ($G$-BSDEs), where
$G$-expectations are constrained in some time-dependent intervals. To establish
well-posedness results, we firstly construct a backward Skorokhod problem with
sublinear expectation, and then apply that in the study of doubly
mean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under
bounded and unbounded terminal conditions. Also we utilize fixed-point
argumentations and $\theta$-methods while solving these equations. Finally, we
extend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with
diagonal generators.
