Unlimited Blade Works: The Guide to the Ultimate Paladin/Sorcerer Multiclass

[Ursus the Grim]

2. Warlock magic is independent, so you get their usual spell free. You can't cast other spells with it, though.

This isn't correct. Pact Magic level doesn't stack with Spellcasting level for total slots available, but you can use the slots from each to cast spells from the other.

Pact Magic.

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.