I'm afraid you need an extra animation for each interaction. Two individual animations - as you have noticed - often lead to strange overlaps.
That means, as was said above: you need an animation that consists of the greeting. Either you cross-fade the animation of the figures as they run towards each other, which almost always leads to interruptions (or the positions are not congruent), or you start with a single overall animation that consists of both figures running towards each other, embracing and then moving apart again. I think the second one is easier - ONE big animation.
Let's say you click on the secondary figure. He stands at a certain start position - at the beginning of the scene, for example. This starts the sequence. After clicking, you direct the game character to a fixed position and direction so that the following cross-fade can start from there without a gap. Otherwise the character "beams" somewhere.The character and the NPC are now hidden, at the same time the new animation appears, in which both characters must of course be standing in the same place and meet each other. It's a bit tricky.
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