Dual boot: How to adjust grub2 settings? Via grub2 in ubuntu or mint?

Question

I have a efi system with a SSD and a HDD. Both these disks use GPT and they each have a FAT32 EFI System Partition (flags = boot,esp) as it first partition. Ubuntu 16.04.3 was first installed on the SSD and Linux Mint 18.2 was subsequently installed on the HDD. While trying to setup a background image and set boot priority for Grub2 in the Ubuntu system, I discovered that despite of what I do there, nothing happens. I then tried to make the same changes in /etc/default/grub of the Linux Mint system and discovered that works.

I discovered this command and ran it from my Ubuntu system:

$ sudo debconf-show grub-pc
  grub-pc/mixed_legacy_and_grub2: true
  grub-pc/kopt_extracted: false
  grub2/device_map_regenerated:
  grub-pc/disk_description:
  grub2/force_efi_extra_removable: false
  grub-pc/install_devices_failed_upgrade: true
  grub-pc/partition_description:
  grub-pc/postrm_purge_boot_grub: false
  grub2/linux_cmdline_default: quiet splash
  grub-pc/chainload_from_menu.lst: true
  grub-pc/timeout: 10
  grub2/kfreebsd_cmdline_default: quiet splash
  grub2/linux_cmdline:
  grub-pc/install_devices_empty: false
  grub-pc/install_devices:
  grub2/kfreebsd_cmdline:
  grub-pc/install_devices_failed: false
  grub-pc/install_devices_disks_changed:
  grub-pc/hidden_timeout: true

grub-pc/install_devices is blank.

Questions:

1. When installing multiple OSes on separate disks, is it normal for the grub2 in the most recent install to take precedence?
2. How do I manage control of grub2 over multiple OS install on separate disks, like in my case? For example, if I dominantly uses Ubuntu and want to have centralise control of grub2 from Ubuntu, how do I do this? My grub2 there isn't responding. Should I do this? The danger of doing this I thought is that if a disk failed, I would still have another disk with grub2 to bootload. Hence, when installing Ubuntu and Linux Mint on separate disk, I had selected the respective disk to install the OSes. However, i am now discovering that managing grub2 in my setup is quite cumbersome to do.

Answer 1

@MichaelBay answered my 1st question. I confirm that here. I had reinstalled grub2 on Ubuntu using the following command:

sudo grub-install /dev/nvme0n1

I reinstalled grub2 because I thought that grub2 in my Ubuntu system was not working and according to @oldfred and here that this command should fix it. After rebooting, I noticed that Ubuntu became 1st in the grub2 menu queue to be boot up. Previously it was 3rd in the queue.

As to my 2nd question, I realize that the answer is just to run the grub2 commands in whichever system I am using, no management needed. Question 2 was motivated by the inconveniences caused by a faulty grub2 in Ubuntu. With grub2 working in Ubuntu, the question was no longer necessary.