Now, in the Child Timeline, the Triforce was never taken by Ganondorf,
Of course it was taken by Ganondorf! Link returned to the Child timeline with Ganondorf sealed in the Sacred Realm, so Ganondorf has got his ToP and Link his ToC.
according to the split timeline theory, there are now two pieces of the Triforce of Courage in the Child Timeline and no pieces in the Adult Timeline.
Completely wrong. There is one ToC in each timeline, logically. Adult Link left his ToC in the future when he travelled back, while Young Link received the ToC of the past as soon as he re-emerged in the Child timeline.
PS: For all of you who think that TWW messes up with the OoT-ALTTP connection, I have evidence that TWW was actually intended to fulfil a major event that is the one overlooked inconsistency between OoT and ALTTP, not to change the timeline as many people assume. I will make a new topic to explain this.
Fine, bring it on.
Does the mark of the Triforce necessarily mean that he still has the Triforce, or just that he once held it?
1) The usual Triforce (birth)mark is just a symbol on someone's hand that has a slightly darker skin tone.
2) The mark of a Triforce bearer, however, is that same symbol *plus* up to three smaller triangles glowing with a golden light.
About 1) we have lots of different information from AoL, Oracles and TP, which suggests that the reasons for its emergence may differ greatly.
We know for sure though how 2) works, namely as soon as someone receives an actual piece of the Triforce, this mark appears with one triangle glowing. So logically, as soon as the Triforce leaves their body again, also the golden glow has to cease. I cannot say if also the darker tone symbol vanishes then, but that's not important for the issue of Young Link in OoT's child ending bearing the ToC.
I've been wondering this for a long time now... Where the hell did that other Triforce of Courage come from?
The Triforce belonging to the adult timeline remained there with Ganon and Zelda while Link's exploded into 8 shards after he closed the road between times. But in the child timeline the entire Triforce is obviously in the sacred/evil realm with Ganondorf who was sealed when Link closed the Door of Time.
So we should assume, yes. But the shining mark means that Link *does* have the ToC without a doubt, so Ganondorf simply can't have it at that point in time

That's all the explanation we get.
This spare ToC is clearly not a birthmark because it is shining on Link's hand, but what's odd is that Triforce part isn't seen in Majora's Mask. Did it go 'dormant' again like in OoT?
No, most certainly the Triforce cannot be taken away from the Hyrule dimension, as this would break the natural laws just as much as taking the Triforce away from a different timeline. Therefore the ToC would leave Link's body as soon as he entered Termina. Staying behind in the Hyrule dimension, the ToC logically has to retreat to the place where it has always been kept, the Sacred Realm. There, however, is now the imprisoned Ganondorf, who is sure to snatch it with glee. That sums it up.
Why? What is this based on?
What Arturo said. And where, do you think, would a released Triforce piece go, if not to the Sacred Realm? Would it go to the Lost Woods, to Lake Hylia or to Death Mountain?!