Does a double replacement reaction involve an exchange of bonds between compounds?
No, it doesn't.
There are two main types of double replacement reactions: a) formation of insoluble ionic substances and b) formation of a molecular substance from the interaction of positive and negative ions.
In case a) the positive part of reacting substance 1 is capable of forming an insoluble substance by sticking to the negative part of reacting substance 2.
Neither ions in reactant 1 nor reactant 2 are changed to yield new species.
there, no ion underwent any change, and neither bonds have got any change or exchanged themselves (they were ionic in the reacting substances 1 & 2, barium chloride and sodium sulphate, and they are ionic also in the product substances, 3 & 4 barium sulfate and sodium chloride.
The only exchange interested the competition between sodium and barium ions to form a stabler and less soluble ionic lattice with sulfate ions.
Being sodium and chloride ions, "spectator ions", this common reaction entailed not really a double exchange, but a single exchange.
In cases b) there is a change in the structure of ionic species caused by the interaction and a consequent partial disappearing of ionic species from the solution to form molecular species as
As an example of reaction type b) let's take a neutralization reaction:
Here the positive part of
We can conclude that in this b-type reaction there weren't any exchange, but just a matching of a positive plus negative ions which combined to form a molecule. One of two ionic bonds in the reactants became a covalent bond in one of the two products (water).
Hope this helps to unveil the true nature of so called "double exchange" reactions.