Is it possible for an airplane to enter another airplane?
Clearly the plane must enter and exit through the belly of the larger plane

Why so? If you drop this condition, things become much easier, because you could attach the smaller planes externally and avoid folding the wings. And this was indeed tried and even used operationally.
The concept is generally termed as Airborne aircraft carrier. The first (?) and most obvious application of the idea was with airships, where the airplanes could indeed be stored internally.

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Russians extensively tried the idea in the 1930s with up to 5 fighters attached on or under the wing of a large bomber.

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Admittedly, this configuration was mostly indended for deployment of the fighters, which would then land normally. This way it was used several times successfully for bombing raids early in the WW2. Recovery of fighters was tried, and some configurations even assembled in the air rather than on the ground. But it was quite difficult and required considerable skills even without any folding wings.
During the tests, on some occasions, there were problems (including at least one fatal incident) you are worried about, namely negative influence of the fighters on the carrier. Mostly they were related to failures, when the attachment broke down or didn't work as expected (sometimes due to incorrect control of the fighter during the process).
However, even pretty much the same idea as yours was explored in the 1970s, with the B747 or C-5 as the carrier and some &quot;microfighters&quot; as the payload. Apparently, the concept was deemed &quot;feasible&quot; but never went to an advanced stage of development. Yet today, the idea may be of some interest again with UAV aircraft.

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