While it is not unreasonable to request a different viva date due to your unavailability, your internal and external may themselves be unavailable at another date. It could be that by requesting a date change the viva may be moved from March to another month altogether. I would seek advice from your university's academic advisory board (or equivalent) and lay out your situation to them. Having said that, if at all possible I would try to stick with the original date. Not that much help I know - it does seem unfair that you yourself have not been officially told the viva date.
Best of luck, I hope it works out for you
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