How do recursive Rope Trick spells work?

Question

You cast rope trick and then you cast it again from within the first extradimensional space. You wait within the second extradimensional space for the first rope trick to end and then for the second rope trick to end. Where do you drop out?

Do you drop out when the first rope trick ends or when the second one ends?

Do the rules for combining magical effects prevent the whole situation?

Answer 1

When the second one ends

The rope trick spell description says:

Anything inside the extradimensional space drops out when the spell ends.

That means that the portal leading to the second one would be shunted to the plane you were on when you cast rope trick the first time. Since you, however, are not in the first space, you are not immediately shunted.

Answer 2

The spell just doesn't say enough

The spell says that "Anything inside the extradimensional space drops out when the spell ends." Are you inside the first space when it ends? Arguably not. So you don't fall out. So you drop out when the second trick ends. Where do you drop out to? Well, the spell is not specific about that, so you have some space for interpretation – I, personally can see it going two ways:

1. The DM does not hate you: you and everything else drop out onto the floor under the first casting of the rope trick, i.e. in your original location. This is just practical and it's the only relevant point in space...
2. The DM hates you and your weird spell bending shenanigans (a real possibility after recursively doing anything): Since the original spot where the second casting could drop you (in this interpretation, this means the first extradimensional space) no longer exists, you are hurled into timeless void appropriate to your campaign setting. Good luck in there!

Note that this is all open to all kinds of interpretations, since the rules are just not that specific.

Final point considering combining spell effects: there are no overlapping spell effects, since the targets of the two castings are two completely distinct lenghts of rope in different time and space.