During a 2v2 can I attack a friendly controlled battlefield?

No, you cannot attack a battlefield controlled by your teammate.

According to Rule 484.8.c, control is not shared in 2v2 games. Furthermore, Rule 484.8.c.2 explicitly prohibits issuing Standard Movement to your teammate's units, and the RiftJudge FAQ (#6609 and #3830) clarifies that allied players' units cannot share battlefields, meaning you cannot move your units onto a battlefield your teammate controls.

Because you cannot move your units onto a teammate's battlefield, you cannot trigger a contest or initiate a combat there.