The following statement does work. But the second command does not work as expected.
ssh root@123.123.123.123 \\"mysqldump -h localhost -u root -pPassWord dbName -d | gzip -cf\\" | gunzip -c > database1.sql
ssh root@123.123.123.123 \\"mysqlbinlog /var/log/mysql/mysql-bin.* --start-datetime=\\"`date -d"1 day ago" +'%Y-%m-%d 00:00:00'`\\" --stop-datetime=\\"`date +'%Y-%m-%d 00:00:00'`\\" > tos1.txt
Incorrect date and time argument: 2009-11-06
_____
update: The problem was solved by escaping the space in the date command.