I'm installing Dolphin emu and I'm not going to have space on my SDD where my Ubuntu install is, so I want to install it on my HDD that way there's more than enough space to download game isos. How do I do this?
You CANNOT change the locations that apt installs to. Those locations are specified when the deb or snap package is created, and are not user-editable.
You CAN change which directories are housed on which drives (or partitions). Your Ubuntu filesystem can be split across multiple partitions by editing /etc/fstab/ and doing a bit of clever copying. Before experimenting with /etc/fstab, be sure to backup your data -- folks make mistakes, and fstab can be unforgiving of mistakes.
For example, using /etc/fstab you can move your ~/Downloads directory to a separate empty partition.