It's a bit complicated, but if Rimuru senses Ainz first, he starts with Anti-Magic barriers within a 30 Mile diameter due to Ainz's magic power.
However, analyzing Ainz and sensing Ainz are two different things. If he analyzes Ainz, he can use to any ability that Ainz does not resist.
Considering the similarity between Reinhard and Hinata, if Rimuru can analyze Reinhard, he will go directly to Gluttony, but before he can reach the size to swallow the Earth or the Sun, he will be erased by Reinhard, just like the situation he experienced with Hinata.
I don't think Reinhard would immediately go for EE against Ainz, but given that Reinhard went for EE with Reid even for a character like Pucks. As soon as Reinhard senses a Gluttony Rimuru that has the potential to swallow the Earth and even the Sun if given enough time, I'm sure he will try to erase Gluttony without caring about Ainz.
So the only reason Pre-Demon Lord Rimuru wasn't erased by Hinata, including his fundemental information, was because Hinata used a small-range attack like disintegration instead of a melt slash attack.
Although Reinhard's AOE EE is not as broken as Hinata's, since he has completely erased Rimuru's physical body and Rimuru is not a Spiritual Lifeform in this key, only Rimuru's core remains and his Spirit rises towards the sky.
Reinhard and Rimuru probably sense each other at the same time, but Rimuru only uses Gluttony after analyzing Reinhard, and Reinhard does not have the information type 2 based haxes to analyze Rimuru's Gluttony before using Rimuru's Gluttony, so Reinhard will only realize that, Rimuru is the biggest potential threat between them when Rimuru uses Gluttony.
With all this in mind, I have the following questions:
1) Will Reinhard fight against Rimuru or Ainz first (who will he turn to first when he senses them)?
2) Does Ainz have something that can kill Reinhard when Reinhard wipes Gluttony?
3) If Ainz kills Reinhard before Reinhard erases Rimuru, who wins Ainz vs Rimuru in 1v1?