I wouldn't recommend that you use two policies to cover one trip as this would be unlikely to give you the cover you need. For a start, most insurers cover 'holidays' or return trips and your existing annual insurer may be reluctant to cover only one part of a return trip.
Secondly, even if they were happy to give you cancellation cover up to the start of your trip, you would not be able to make a claim if you had to cut your holiday short because of your mum's deteriorating health. The best option is probably to talk to your existing insurer and see if they will insure you for another full year.
Some insurers would refuse to offer full cover for 12 months (including curtailment) because your mum has already been in hospital, but some companies may consider it. If the insurer accepts you it's likely to be more expensive than your current policy, although without knowing more about your situation (such as the premium you paid and your mum's state of health) I couldn't say how much extra you might have to pay.
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