2 Linux OSes with 1 GRUB and a low-latency kernel

I have Deepin OS and installed Ubuntu Mate as the third OS for recording and KXStudio addons. When I installed Ubuntu Mate, I typed ubiquity -b in the terminal to avoid installing grub. I did this because the Deepin GRUB theme is really nice (hint Ubuntu), and if I install Ubuntu with GRUB, I will lose that Deepin GRUB theme and the ubuntu GRUB will be the active one. Then the Deepin will think it is using a GRUB but it is not "connected" and Ubuntu will use a GRUB that is connected. Since Deepin is my main driver, I want to keep it connected to its GRUB.

So right now, I have an Ubuntu grub that is not connected to the boot grub. After install of Ubuntu Mate, I did an update-grub while in the Deepin terminal. This added an Ubuntu entry to the Deepin GRUB. After installing low latency, update-grub did not change anything and it still boots generic kernel when I choose Mate from the Deepin GRUB menu).

How do I manually add the low latency to the Deepin GRUB I am using now assuming GRUB is GRUB? Normally, simply installing low latency will add it to GRUB. But it adds it to the wrong GRUB files.

What file do I edit and how? Deepin has a boot directory, /etc/grub and /etc/default folders inside the root. I want the Ubuntu boot menu to choose the low-latency kernel instead of generic. (I use uname -r when in Mate.) Mate also has the same boot and GRUB folders inside the root dir.