What do you call someone who is emotionally strong?

I was originally going to suggest "Stoic", "Stalwart" and "Unflappable", but they won't work since you're looking for a specific noun. (Though, they're still good adjectives you should look into.)

You might say "Pillar of Strength" here, or perhaps even "Foundation" (Though foundation is typically used for ideals in this sense). These words evoke images of steadiness in troubling times and are usually equatable to people who are emotionally strong, bearing any hardships without breaking under pressure.

I don't know if there is an exact word for an emotionally strong person, but as allusions, these will almost certainly convey what you want.

In this particular context

anchor

A person or thing which provides stability or confidence in an otherwise uncertain situation

Or possibly

keystone

The central principle or part of a policy, system, etc., on which all else depends