Newborn necessities at second home?

My baby's father and I don't live together as of now, and when our baby is born in September, the baby will primarily be living at my place. We will be visiting him at his place frequently, but my question is, what baby items should be at his place? I don't want to be lugging a whole bunch of stuff around everytime I go. And I don't want us to have to spend too much extra money having to buy items twice, so what are the necessities? The only real thing I can think of is a binet for when we have an overnight stay, and of course bathroom items that I will have in my diaper bag. Thanks.