So, as a divine soul sorcerer, if I were to dip into a cleric domain, would I need to prep the domain specific spell per cleric casting rules, or can it still be cast as a sorcerer would?  For example, a Forge Cleric gets Identify at lvl 1, would I have to prep that prior to casting, since its not in either the sorcerer or the cleric spell list?

Short answer: no, you do not need to prepare the domain spells, but that's because clerics do not need to prepare their domain spells - they are always prepared. 

For reference, let's check the Spellcasting rules in the Multiclassing section of the PHB. It says:

You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.

So you'll follow the normal cleric rules for preparing spells for any spells you would get from your cleric level. Let's double-check what those are for domain spells, found here:

Each domain has a list of spells — its domain spells — that you gain at the cleric levels noted in the domain description. Once you gain a domain spell, you always have it prepared, and it doesn’t count against the number of spells you can prepare each day.

If you have a domain spell that doesn’t appear on the cleric spell list, the spell is nonetheless a cleric spell for you.

So if you multiclass 1 level into Forge Cleric, you'll always have Identify and Searing Smite prepared, along with your cleric level (1) plus your wisdom modifier in additional spells from the cleric list. 

To answer it another way, your domain spells that you gain from having a level in forge cleric do not interact in any way with your divine magic feature; they are not added to the list of cleric spells that you can access by being a divine soul sorcerer.