Broadcast with Limited Spreading
Canonical solutions to the broadcast problem include, as you mention, flooding (controlled &amp; uncontrolled, although uncontrolled flooding is untenable for a variety of reasons), as well as spanning-tree based approaches and N-way unicast (which is basically just to point out that broadcast protocols don't represent fundamentally more powerful communication mechanisms).

What you're asking about sounds somewhat similar to a sort of controlled flooding with fault tolerance. Alternatively, you might conceive of your scheme as a spanning-tree approach where multiple redundant spanning trees are defined for each node. In fact, a hybrid of these approaches would help avoid loops, explosion, etc.

Kurose and Ross provide a good explanation in their book "Computer Networks - A Top Down Approach", which you might use to develop your own broadcast protocol.