You always use the DC of the spell, unless said otherwise.
You don't have to recalculate your con bonus, calculate your HD or anything, simply use the spell save DC for any abilities that require a saving throw.
From Transmutation (Polymorph):
Each polymorph spell allows you to assume the form of a creature of a specific type, granting you a number of bonuses to your ability scores and a bonus to your natural armor. In addition, each polymorph spell can grant you a number of other benefits, including movement types, resistances, and senses. If the form you choose grants these benefits, or a greater ability of the same type, you gain the listed benefit. If the form grants a lesser ability of the same type, you gain the lesser ability instead. Your base speed changes to match that of the form you assume. If the form grants a swim or burrow speed, you maintain the ability to breathe if you are swimming or burrowing. The DC for any of these abilities equals your DC for the polymorph spell used to change you into that form.
Reading Elemental Body, we have the following:
When you cast this spell, you can assume the form of a Small air elemental, Small earth elemental, Small fire elemental, or Small water elemental. The abilities you gain depend upon the type of elemental into which you change. Elemental abilities based on size, such as burn, vortex, and whirlwind, use the size of the elemental you transform into to determine their effect.
Air elemental: If the form you take is that of a Small air elemental, you gain a +2 size bonus to your Dexterity and a +2 natural armor bonus. You also gain fly 60 feet (perfect), darkvision 60 feet, and the ability to create a whirlwind.
As we can see, there is nothing replacing the more general text from the Polymorph subschool. Meaning that we use the DC of the spell used to assume the elemental form.
This can be seen on other spells, like Form of the Dragon's Frightful Presence ("DC equal to the DC for this spell").
Monkey in Leather
I take roughly humanoid to mean "a being resembling a human in its shape." One way to estimate that is by judging a sillouhette. Here are the beasts whose sillouhette could reasonably be mistaken for a human's by someone not overly familiar with anatomy.
The Moon Druid also gets access to Elemental Wild Shape at 10th level and the elemental forms may be roughly humanoid (ask your GM if they are). Keep in mind that these forms are Large so you may need different sized armor or magic armor to account for the size difference. Also, some of the forms have more useful natural armor anyway.
Best Answer
The Monster Manual and DMG have 2 possible solutions to this:
you could treat it like the same mechanics that the Tarrasque (MM p.286-7) uses to swallow, but scaled down to whoever swallowed the druid, or
use the "inside an object" (as in the Daern's Instant Fortress) mechanic from the DMG, where both would take force damage based on their size: most likely 1d10 if they were both medium humanoids.