Go ahead and cut out any dead branches on any of your shrubs.
Regarding the yellowing, check out which leaves are turning yellow. If young leaves near the tips are yellowing while older leaves remain green, your plant is exhibiting iron deficiency. If older leaves are the ones yellowing and dropping, the problem may be soggy growing conditions which can destroy roots by cutting off their supply of oxygen. Nitrogen deficiency shows up as yellowing of older leaves first and in time can progress to all the leaves on a plant.
Other causes of yellow, dropping leaves are drought (which doesn't apply lately!), herbicide injury, and physical damage to plant roots.
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