I'll give you a bit more perspective. (If you already know this....then....never mind
)
You're using a single speed, coaster brake type wheel/hub and putting it on a frame that was meant for a multi chain ring/derailleur type wheel/hub.
The hubs that are meant for multi chain rings, called "Freewheel" hubs are wider than single speed hubs. So that means that the axles are longer. And that also means that the dropouts in the frames of multi-geared bikes are wider.
Maniac's advice about bending the frame in to fit your new axle is just fine. It ought to work for you.
But if you follow WheelBender's advice to get a new axle, then you'll have a chance here to practice another skill you're going to need. You see, those coaster brake hubs, in this application, need a bit of attention.
I'd start by trash-picking a bike with multi chain rings on the back hub. That axle will fit your frame. Or just buy a wheel from one of the sponsors of this site. They're not expensive. Some of the sponsor might not carry these wheels. But I think one or two of them do.
Now you want to switch the axles.
Have some clean rags or paper towels on hand to place parts on. Have some more rags or paper towels handy to wipe grease off of your hands.
Start disassembling your coaster brake axle. As you're pulling it all apart, pay attention to the parts in there. It's not really all that complex and it's not really all that hard. But it takes a bit of practice to get familiar and to put it all back together again.
Clean out the old, dirty grease inside that hub and replace with fresh grease. I think you can pack just as much in there as you want to without causing harm. (Will someone correct me if I'm wrong?)
Re-assemble using the axle from the other wheel. Disassembly of that wheel will be less worrisome. A simpler hub with fewer oddball parts.
You might as well start watching the street curbs for thrown out single speed bikes (wheels) as well. These are a good source of spare hub parts. They might come in handy.
I'd recommend cleaning and re-greasing that hub about once per season. On a motorized bicycle those coaster brakes live a hard life. It's not hard to toast one.
I'd recommend putting rim brakes on both wheels as well. That'll take some of the load off of that coaster brake. And with that set-up, you'll have very good braking. I've done it and I've been pleased with the results.
If you're really, really 'green' (new at this) and you don't know how to start taking a hub apart, then come back and say so. I'll do a disassembly and take photos and post it all here.
Sunday morning (Dec 14) would be a good time for it.
