I think the answer is quite simple. The most important rule, in claiming a minor child, is where they lived. Since they did not live with you for more than half the year and they DID LIVE with their father for more than half the year, you cannot claim them.
Rule #1, in the other answer, includes "cannot be the qualifying child of any other taxpayer". The children are the "qualifying child" of their parent with whom they lived most of the year.
You cannot claim them, even if the father was willing to allow you to, unless the father is not required to file a tax return (basically his income is under the filing threshold). Even then you would have to meet the support test (#4), which is unlikely since you had them only three months
