Moorcrys
Explorer
Transmuted Spell metamagic from Tasha’s might help with the fire issue. Maybe a bloodwell vial to give them a few extra SPs as well.
Also - if you don’t want to add some spells known to the dragon sorcerer to bring them in line with the design of the newer bloodlines, you might want to consider having their sorcerer find some kind of a staff. That will give them some extra spell versatility (heck you can design the staff to give them access to a few spells you think would really help them if you want) that’s thematically in line with their class choice. Staffs are awesome for sorcerers imho.
Also - if you don’t want to add some spells known to the dragon sorcerer to bring them in line with the design of the newer bloodlines, you might want to consider having their sorcerer find some kind of a staff. That will give them some extra spell versatility (heck you can design the staff to give them access to a few spells you think would really help them if you want) that’s thematically in line with their class choice. Staffs are awesome for sorcerers imho.