The source of all conflict within the money-laundering organization came from a single word, profit.
Credit needed to be given where credit was due. It was due to Edward's presence in the organization that such conflicts could be resolved with such expediency.
Madam Grace had one or two nemeses in her life, and the reason for the hatred or the process leading to that hatred was not really that important. The important thing was the unsteady relationship that pitted them against each other for the fight for power and resources; the time that they had spent 'working together' did not help the situation either. It was an open secret that they could not wait for the other to die. Even if they belonged to the same organization, it would not have been so surprising to wake up to the news that one had already killed the other.
Why would one expect anything else with the expert discord sower working next to Madam Grace?