You should take care of your visa in advance. You can cancel your Estonian visa and apply for a visa for the whole period of your trip.

Schengen visa can be extended in case of insurmountable circumstances, other serious professional or personal humane causes that have arisen after the visa has been issued, and which do not allow the alien to leave the Schengen territory before the expiry of the visa's validity term or in connection with the end of the period allowed in it stay. Such an extension is provided free of charge. Extension of the validity of the visa can not exceed 90 days.

In Latvia, the visa is extended at the Citizenship and Migration Board of the Ministry of Internal Affairs of the Republic of Latvia. This competent authority is authorized to extend the visa even if the applicant travels to the territory of another Schengen country than the country in whose territory he is applying for the application. But, of course, if it is possible to do this in Estonia - it will be better.