Second Linux installation ate the splash screen animation of the first Linux installation
 

In the grand scope of Linux problems, this is not that earth shattering, but it annoys me to no end.

I have a dual Linux boot system. I fully expected that my second installation would make itself the dominant OS on grub (first grub choice and default Linux to boot). What I didn't expect was that it would remove the boot animation of my other Linux installation.

Can there be only one splash screen boot animation? Is there a way to return the boot screen animation to my initial Linux installation?

For what it's worth, my initial installation is Scientific Linux to which I added Ubuntu. Apparently, Ubuntu really likes to take over.

Also, is there a way to change the order of the operating systems listed by grub to make Scientific Linux the default OS?

What you experienced is the same thing that happens when installing Windows: usurpation of the MBR on an MBR system, or usurping priority on a UEFI system. All Linux distros I've installed default to installing their non-UEFI bootloaders on the MBR. Most offer an installation option to not touch MBR code. On MBR, whichever Linux you wish to control boot should put its bootloader one of two places:
The other distros need to have their bootloaders either on their /, or a separate /boot/ exclusively used as its /boot/, or nowhere. With #2, its mounting options would be /, or /boot, or, if you wish to exercise manual control of master boot, elsewhere.

On UEFI, either go into BIOS setup and switch the priority as desired, or utilize efibootmgr.

Thank you so much for your help. I can live with the boot order as it stands, though I wish it were different and I may apply your suggestions, but what I'd really like is to get the boot animation back for Scientific Linux. Is there any way to do that?

The easy way: wait. Eventually Scientific Linux updates should include a bootloader update that will reinstall the bootloader. If you can't wait, reinstall the bootloader yourself. I don't use SL, so won't presume to know the exact steps to take to do so. It might be as simple as logging in as root and then running

The simple fix is to get the SL boot code in control. Looking at this Fedora, I doubt the above command will work.
However the correct command may depend on:
- the version of SL
- the version of grub (depends on the above)
- the device firmware (UEFI or BIOS)

None of which we know. Whilst the fix is simple, screwing with the loader and making the machine non-bootable generally causes more angst than benefit.

Well, I played around with it yesterday to the point the machine really was non-bootable. I decided to re-install Scientific Linux, thinking that it would detect the Ubuntu installation and things would be made right. Well, on the surface that is what happened, but it would not boot Ubuntu from the boot screen. In the end I wound up installing Ubuntu again too. Now the system is working and I'm not going to mess with it further. Lesson learned.

I still have no splash animation with SL, but I no longer care.