meanwhile是副词,在这里有2种写法.
Mother went shopping .meanwhile,I cleaned the house.
or
Mother went shopping.meanwhile I cleaned the house.
前面一个必须是句号,因为除非有如but,because表示句子关系的连词,否则同一个句子里不能出现2个主语2个谓语.
如果想不明白可以参照其他副词的用法.如：
He try to get rid of that.Unfortunately,he failed.
He try to get rid of that.Unfortunately he failed.
还有疑问可以参考我下面附的外国网站相同问题回复,有几个老外给的meanwhile例句