First of all, the number of frames in each of the GIFs you want to combine need to have a common factor so that they can loop neatly.
For example, Animation 1 has 50 frames:

Animation 2 has 25 frames:

These will work because I know Animation 2 can play through twice exactly in the time that Animation 1 plays through once.
Now I'm going to import all the layers from one document into the other, so they're all together. You'll find it easier to import the shorter animation into the longer one.
Select all the layers, then drag them onto the "Create a new group" button:

Right click the group, and choose Duplicate Group.... Select the document containing the longer animation in the drop-down list and press OK.

Now you've got all the Animation 2 layers in a group, sitting above the Animation 1 layers.

Now comes the tedious part.
Basically you have to go through, frame by frame and cycle through each individual layer of Animation 2.
Frame 1, make the first layer visible

Frame 2, make the second layer visible

Frame 3, make the third layer visible

...and so on. This might take you a long time if you're working with a large animation.
Here I've got to Frame 25, which is the halfway point of Animation 1, and the final layer of Animation 2.

This is where Animation 2 will start its second playthrough.
Frame 26, make the first layer visible

..etc, all the way to the end.
Because all of Animation 2 is in a layer group, I can manipulate it easily.
Here I've gone back to Frame 1, selected the group, and pressed Ctrl+T to transform the group.

I've moved Animation 2 over to the left, now I'm going to apply a gradient layer mask to it, to reveal more of Animation 1 sitting underneath

And that's it!
Final GIF:























