More train related than you think.
Don't worry about posting the question here. The specific subject may not be train related, but the general issue definitely is. I use these techniques to modify and repair parts all the time.
Sometimes a replacement is the best option. However, if repair is the desirable route, I agree that you need to reinforce the joint somehow. Most glues are not all that strong on their own, so you'll want to add something mechanical to secure the joint.
First of all, can you devise a purely mechanical means of holding the broken part together while keeping it functional? For example, of there are reinforcing ribs which run across the break, perhaps you can drill holes in some and use wire, string, or cable ties to hold them together? Or, you may be able to add a filler block with screws from the outside (flat head and countersunk to avoid any protrusions). Once you do that, then you can add a good two part epoxy (I'm fond of J.B.Weld) to make sure the joint is solid and secure.
If you cannot do that, can you add a brace which spans the joint, either internally (drill holes and insert brass rods) or externally (glue plastic or metal plates/strips across the joint)? That will go a long way toward making the joint stronger, sometimes as good as new.
Finally, take time to treat the surfaces which the glue will touch. Rough them up. If possible drill holes through them. Imagine that the glue will not bond to the plastic at all, but will only serve as a free-form filler (not true, probably, but useful as a worst-case thought experiment). If you can make it mechanically interlock with the parts in some meaningful way, the joint will be stronger and less likely to fail again. And of course, surgical cleanliness will help as well, as a lot of plastics are difficult to bond to at the best of times, and kids toys collect dirt on interesting places.
