I wouldn't bring them into the house... at least not initially. In this weather with my furnace running, my house is between 26 and 29% relative humidity. All of my bow wood, including a pile of osage boards, is out in the garage, drying slowly. I may bring it in to finish bringing it down the last few percentage points, but I wouldn't bring it in there green.
Just see what you get back from the mill and then go from there. There may be no need to reduce it further. I have bow wood lumber in all shapes and sizes. Just tell him you want it at least 2" wide, that way if it warps a little bit, you may still have room to get a straight piece out of it. I often cut them 2.25 - 2.5" initially to allow for that, then if they don't move, lams can be cut from the side as well.