If I use Evelynn Entrancing to move an enemy Irelia Fervent to my battlefield I'm holding from face down, I also have a Mutated Mouser, does my Mouser get the defend buff as I am defending or am I technically the attacker since I forced the Irelia to fight?

To answer your question, we must look at how you initiated the combat and the combat designations.

1. Attacker vs. Defender

According to RiftJudge FAQ #5394, #7275, and #8263, when you use an effect (like Evelynn, Entrancing) to move an enemy unit to a battlefield you control, that enemy unit becomes the attacker.

Even though you played the card and initiated the move, the enemy unit is the one entering your controlled space to contest it. Therefore, Irelia, Fervent is the attacker, and you are the defender.

2. Mutated Mouser’s Shield 2

Because you are the defender in this combat:

• Your Mutated Mouser has the Shield 2 keyword, which grants it "+2 [S] while I'm a defender."
• Since you are the defender, Mutated Mouser will get the +2 Might buff from its Shield keyword for the duration of this combat.

Summary of Events

1. You reveal Evelynn, Entrancing from face-down on a battlefield you control.
2. Evelynn’s ability triggers: You move the enemy Irelia, Fervent to your battlefield.
3. Because your opponent's unit is moved to your battlefield to contest it, Irelia, Fervent is designated as the attacker, and you are the defender.
4. As a defender, Mutated Mouser's [Shield 2] ability is active, granting it +2 Might.

Note: This interpretation is based on established FAQ rulings regarding moving enemy units to your battlefield (RiftJudge FAQ #5394, #7275). While no specific FAQ exists for this interaction with Evelynn, she follows the same mechanic as other move effects.