Automate & schedule MS SQL database migration & backup

I need a solution to Automate & schedule MS SQL database migration and backup. I have 2 websites that are running on 2 different shared hosts. Their databases are also running under those 2 different shared hosting accounts. I need a solution so that these 2 databases always have same data. If one database gets updated, the other one needs to be updated right away. I also need to be able to save backup of this database on my local computer in an easy way. There are expensive software available on the market that does these kinds of jobs, but I need a cheaper solution if you can provide any.