While I have no experience with the Canadian Red Cross, experience with its U.S. counterpart provides precedent worthy of consideration.
The American Red Cross takes in the bulk of all charitable dollars after disasters, but uses spending practices which are purposely opaque. Having taken in 32.7% of corporate and foundation dollars in the immediate aftermath of Katrina and more than half of the donations from individuals (between $2.1 - 2.7 billion according to different reports), they designed programs at the national level with negligible levels of local input - programs which quickly showed themselves to be ill-suited to the needs of the population they intended to serve. Local Red Cross affiliate staff vigorously protested national policies.
Efforts to change this programming to make it more responsive to local realities using evidence-based assessments met with resistance at the national level, but did eventually produce reforms - a process that took 18 - 24 months. Other NGOs were nimbler in their adaptations and showed greater humility when facing the need to adapt. As time passed, continued criticism resulted in a protectionist instinct and the organization turned inwards to focus on 'brand' and legacy. Furious efforts to spend down Katrina accounts and shut down programming generating controversy ended this foray into recovery.
Quite interesting is the fact that the Red Cross takes in more funding than it can effectively give out, so in terms of recovery (not response/relief) it becomes a donor to other NGOs - providing grants (many to further Red Cross goals which the organization then also takes credit for, and others to completely independent and original projects - many of which have been groundbreaking in past disasters). Within the NGO community, the additional Red Cross role of donor further exacerbates tensions over donations and brings in issues of control over NGO agenda-setting.
Georgetown University, Emergency and Disaster Management Program