Beginning of Dominance

The first thing that happens in the Dominance phase is that each player counts their standing STR. The person with the most STR claims 1 power for his House. If there is a tie, no one wins dominance, and no one claims power.

Jaime has 2 standing STR (Lannisport Steward), while you only have 1 (Sansa Stark). He claims 1 power.

Jaime claims Dominance (1 power goes on his House)

That's normally it for the dominance phase. But wait - your opponent kneels his 2 locations and plays an event card:

This event has the word Dominance in bold: this means that it can only be played during the dominance phase. Weapons at the Door has a 3 influence cost. Jaime has exactly 3 influence (the scroll icon) total on both of his locations - Fallow Fields and Queen Cersei's Chambers. So he has to kneel them both.

That's the cost of Weapons at the Door. The effect is to discard all of your attachments. Crested Wolf Shield goes into your discard pile. The duplicate of Sansa Stark stays, however. Remember, duplicates do not count as attachments.

Jaime plays Weapons at the Door to discard your attachments

That's a pretty mean move by your opponent. But wait - you have a dominance event of your own!

You have no influence, but the event has an alternate cost - kneeling a character with the Noble Crest. Look at the bottom right corner of Sansa Stark - she has the Noble icon. Kneel her to pay the cost. Now for the effect - choose a non-Stark character to die! Let's execute Cersei Lannister.

You play Guilty! to kill Cersei Lannister

She goes into the dead pile, and since Cersei Lannister is a unique character, your opponent cannot play another copy of her.

Dominance is over. One more phase to go in the round!