Data mirroring MS SQL 2008 R2

I have problem with database mirroring. I have 2 servers on both I have installed SQL Server 2008 R2 and on both I created the same user name and password.

Db mirroring is working if I use "This account" option (look at picture).

If I use "Built in account" db mirroring is not working.

The problem is because I am using other tools for redundancy, which also need SQL Server. Redundancy doesn't work if I change "Built in account" option to "This account" option.

How to solve this problem?

Thank you