Both the Toy Plane and the Train share similar problems with it bugging out whenever you try to mount them. They usually get stuck without explanation and, try as you might, feel frustrated with this bug.
Fear not, for I have figured out a method that works 80% of the time. These methods are almost a guarantee for successful mounting.
Toy Plane:
The toy plane is a lot trickier to manage than the Train but is nonetheless capable of being able to spawn successfully. Here's two ways to spawn it:
1) Walk and Press M simultaneously. This will allow you to gain control of the plane once its starts up so that it doesn't stay still even with you pressing W.
2) Jump, Walk, and Press M simultaneously. Sometimes, the first method doesn't work depending on what happens to the Toy Plane (explosion or successful landing). In this case, you will also have to jump, press W, and press m at the same time for it to finally be able to fly.
Train:
Train is a lot more simpler. There's actually just one method to spawning it successfully.
1) Walk and Press M simultaneously. Most of the time this method works. You will instantly start to ride the train and it also removes the bug where the train immediately falls after you spawn it, forcing you to wait until it's back up again.
Hope this guide helps you all in spawning these mounts without much interference.