Jim and Ed have given you the best advice so far.
I will try to add a little more to help.
First off, this is not a 30amp breaker. Its called a duplex breaker (sometimes known as a 'peanut breaker'). It has 2 15amp breakers that occupy the same space as a 'normal' breaker. It would be referred to as a '15/15 duplex breaker', not a 30 amp breaker (that is a whole different animal and should never be on a circuit for your standard receptacles.). These are actually separate 15amp circuits.
Second, please carefully check the bus (where the breaker plugs into the panel). It is likely an aluminum bus. If it is heat-damaged / burned in any way, do not re-use this space. You will need to move to an empty space (hopefully you have one). If you re-use a burned tab on an aluminum bus, the replacement breaker WILL fail prematurely (I've seen them go in as little as a week).
Here is a list of common mobile home panels for that era (that I am aware of) and their modern replacement:
Panel:
ITE
Gould
Crouse Hinds
Modern Replacement: Siemens, Type QP?
Panel:
Bryant
Westinghouse
Murray
Arrow-Hart
Modern Replacement: Cutler Hammer/Eaton, Type BR
Panel:
Square D
Modern Replacement: Square D, Type QO (Square D "Homeline" was not around that far back)
If you have some other type of panel, please update the post. I'm sure that one of us will come up with the correct answer for you. If the panel says "Zinsco" or "Federal Pacific", plan for a new panel.
UPDATE:
Now we have something to work with. First, have you tried resetting the breaker? Move the handle all the way to the off position. Then try to turn it back on. If that doesn't fix it, read on.....
Assuming that this is the original panel for this home, the breakers are known as Type QO. You are looking for a QO Tandem breaker (I believe the breaker you need is a "QONT 15/15"). The new ones will look a little different. The old ones had breaker handles that were side-by-side (when the breaker is viewed horizontally). The new ones have the handles one above the other.
Hope it works