Target directory of built in backup funcionality

I'm using built in backup functionality (whole system image) and I've scheduled it to every week on Sunday. The image is coming with two files and a folder in the main catalog of the D: partition (secondary disk), where I have a lot of other files and folders and it's pissing me off cause I need to move them to the Backup folder every week manually. Is there any possibility to change the target directory of the backup?
I would like to have these files automatically moved when it's done or (better) created in the D:\Backup, and sorted by date in folders like D:\Backup\2014-01-05\ - for backup from last Sunday and D:\Backup\2014-01-12 - next Sunday, 2014-01-19 after next and so on.

I've read about scripts and add parameters in wbadmin but I can't things like that and it's telling me nothing.

Windows Backup saves into the drive letter:\computer name\Backup Set YYYY-MM-DD HHMMSS folder.

A System Image saves into the drive letter:\WindowsImageBackup\computer name\Backup YYYY-MM-DD HHMMSS folder.

That's how it looks now and how I don't want to be. Thought there was some scripts which I read about possibilities by them.

Do you really mean that I can't even move every backup, when it's done (in the same structure like original) but to D:\Backup where I want to have them all stored to not messing up my HDD in the main partition lik now? In that Backup folder I want to manualy create other folders with name of that day they have been created and just move them there so I've everything sorted by date.

I've another question. Can I securely disable Windows Backup service (is there more than just this one?) when I decide to go with third part backup program? If it matter so I thought Paragon Backup & Recovery will be fine for me. Heard it is quite good soft.

Thanks! Will check out Macrium. Never heard about this.