Yes. Enter the child you are claiming as "The whole year."
You can use 0 months the second child. However you don't have to list the second child on your tax return if your wife is claiming the second child, unless you want to be considered the custodial parent and claim some tax credits.
If you are claiming both children 50/50 it seems you should only be the custodial parent of one child and your wife the custodial parent of the second child. It would be easiest to leave the second one off your tax return.
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