Each installer/player is independent of one another. Installing one player type will not uninstall the other player type. I suspect there's an issue with your installer script that's not installing all 3 player types.
What os versions are you installing on?
Please provide the FlashInstall.log file from an impacted system. The file is saved at C:\Windows\System32\Macromed\Flash. If the system is a 64-bit system, there's another FlashInstall.log file saved at C:\Windows\SysWOW64\Macromed\Flash. Both files are required from a 64-bit system. Upload the file(s) to cloud.acrobat.com/send using the instructions at How to share a file using Adobe Document Cloud and post the link to the uploaded file(s) in your reply.
Are you using the EXE or MSI installers?
I created a policy on Windows Server 2008 using Group Policy Management. In policy in Computer Configuration\Policies\Software Settings\Software Installation I created 3 installers from msi files (downloaded from adobe) - everyone for another browser. When I restart computer i see that pnly one is installing (NPAPI). I check on Control Panel\Programs and functions and on list of programs is only one - NPAPI. Why?
Please provide the previously requested information. For the FlashInstall.log files, If the files are from a 64-bit OS, please append system32 to the file from the C:\Windows\System32\Macromed\Flash directory and syswow64 to the file from the C:\Windows\SysWOW64\Macromed\Flash directory.