There is no way a dependent can live 51% with each parent. You go with the one considered the divorce deemed custodial parent or figure the percentage child was with each parent and do the support worksheet to determine which contributed more support.

Whatever the options turn out to be...it is your client, not you, who makes the final decision on reporting. 

The custodial parent is not required to provide an 8332 and you cannot include it on the return unless signed by custodial parent.