This question brings up a number of different issues.
HaRav Elyashiv shlita is of the opinion that one may not ignite a new fire solely for the purpose of saying the beracha at Havdala on Yom Tov, since one has no intention to derive any personal benefit from its light. HaRav Shlomo Zalman Auerbach zatzal was similarly doubtful about its permissibility. However this issue can easily be circumvented by using the existing Yom Tov candles for Havdala, and not lighting a new one.
The next issue is tilting the candles and holding them together , which inevitably causes more wax to melt and drip off. While the Taz 514:2 forbids one to tilt a candle on Yom Tov to make it drip because of gram kibuyi, the majority of the Achronim disagree. Additionally, the Taz himself was only referring to a situation where the expressed intent was to cause the fire to extinguish sooner, which is not the case here.
The biggest problem is separating the candles at the conclusion of Havdala. The Rema 502:2 writes that one may remove a burning stick from one side of a bonfire to place it in the fire on the other side, even though the intensity of the fire will inevitably be temporarily diminished, since the reduction of the fire is not intentional. The Mishna Berura sk 20 adds that based on this logic one should similarly be allowed to remove the stick to light the way in the dark as a torch. So it would seem that there is no problem separating the candles after Havdala. However, the Mishna Berura adds that some Poskim disagree with the Rema's heter and forbid removing the stick, and one should be machmir for their opinion, and the Shulchan Aruch HaRav concurs with this stringency. It would appear that the same should apply to our Havdala candle, and one should be machmir, however the prevalent minhag is not to.
While it is evident that holding the candles together is permitted in Halacha and it is only a chumra to refrain, one must weigh against this the fact that using a torch or other multi-wicked flame for Havdala is only a "mitzva min hamuvchar" as the Gemarra Pesachim writes; a chumra itself.
So it seems to me that if one has a specific minhag to hold two candles together for Havdala on Yom Tov, it is permitted and not necessary to change an established and legitimate minhag. However a person who does not know of a definite family custom would be better served keeping the candles separate for the duration of Havdala.