"Alternate Mondays" is fine. However, your request doesn't really make sense. If you want to go to the gym early in the morning, surely you could work from 10am every Monday. Are you only planning to go to the gym on alternate Mondays? I'm confused as to whether you are requesting a change to your normal Monday working hours but only on alternate Mondays, or if you are asking to work two Mondays a month and have two Mondays off every month.
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