i remember you 这个句子正确吗

正确的。

属于"forget/remember somebody('s) doing something"的句型

也就是remember+逻辑主语+动名词，即remember+动名词复合结构

但是口语中，your比you不常用。

I remember you playing the piano.

I remember your playing the piano.

I've forgotten you saying that to my sister.

I've forgotten your saying that to my sister.