I have a shared custody arrangement with my oldest daughter. She is with us every other weekend. How long should I say she "lived with me"? 12 months? 3?

WITH your daughter, or FOR your daughter?

I assumed the arrangement was with the other parent for the oldest daughter.

Count up how many actual nights she stayed with you.

Divide the number of nights she stayed with you by 30. That is approximately how many months she lived with you.

Or do this:

2 nights every other week equals 52 nights per year.

52/365 = .14.25%

.1425 x12 = 1.71 mos.

You are not her custodial parent, since you had her less then 50% of the time.

This will give the correct answer in turbotax.  Because you don't have custody more than half the nights of the year, you can't claim her as a dependent unless you get a signed release.  By figuring your custody in this manner (4 nights per month= about 2 months) turbotax will give you the correct options in the interview.

"You are not her custodial parent"...and therefore you cannot claim her as a dependent on your tax return (unless the custodial parent releases to you his/her right to claim her, or it's spelled out in a pre-2009 divorce agreement).