Is my interpretation of "向右往后勾提。至甲势已背时" correct in the context of Tai Chi?
first of all

a two-person push hands sequence

the mentioned verse is of sparring (散手), not push hand (推手)

甲 is the left man, grey cloth; 乙 is the right one, white cloth

乙被掤・乘勢含胸拔背・向右轉腰坐腿・右手刁住甲右腕・向右往後勾提・至甲勢已背時・右手按甲右腕・同時左手按擊甲右肩

[乙’s ] right hand stick with 甲’s right wrist (右手刁住甲右腕)
towards 乙’s right and aft [向右往後], connected [hand and wrists] (勾), slightly upward (提); till (至) the moment that 甲’s posture (勢) shows his back (背)
the hidden message is: 乙’s wrist, arm moves according to the turning of waist and shifting centre of gravity (轉腰坐腿)

as &quot;Face to the right and shift back, drawing out the force from #1's back until none is left.&quot;


Does my translation of &quot;勾提“ make sense in this context

nice try  well, i’m sorry to say, no.
btw, here’s a wordpress page, you may find helpful info:
https://brennantranslation.wordpress.com/2011/07/11/taiji-two-person-sparring-set-taiji-san-shou-dui-da/
have fun :)