I will start by saying there are several subtly different definitions of the verb depend, but for the purpose of this answer I will focus on two of them.
- (Actually two slightly different definitions, but sufficiently similar in usage for my purposes) to rely upon for support or maintenance; to rely/place trust.
- To be conditional or contingent on something.
Will be depending can only be used in the sense of definition 1, it is at the very least not idiomatic in the sense of definition 2, and may be grammatically incorrect (hopefully someone can point out a reliable resource that says whether it is "against the rules").
The best way I can think of explaining it, is as follows.
- In definition 1, the state of something remains as it is, and relies upon something to keep it that way. Therefore the verb "be" is appropriate, because the state is dependent.
- In definition 2, the state of something might change and the change will be contingent on something. Therefore, "be" is not appropriate, but "change" could be ("Our return date will change depending on the cost of airline tickets.") because the change (not the state) is dependent.
An example to attempt to explain the subtle difference:
I will be depending on the weather tomorrow. - I am relying on the weather doing what I want it to.
The kick-off time for tomorrow's match depends on the weather. - The kick-off time might change, and the condition determining the change is the state of the weather.
In your examples you are saying that the return dates are contingent upon the cost of the airline tickets, so you can't use "will be depending". As FumbleFingers said, you can use will depend, or more idiomatically depends. You can do this because the return date has not been decided, so, as well as being dependent in the future, it is also currently dependent upon finding out the costs.
Also, as FumbleFingers said, you need a determiner [an/the/our] before "airline ticket", unless you pluralise "ticket" to "tickets", when you don't need a determiner.