It depends a lot on the size and shape of your tiers. I have often taken 3 tier cakes stacked as far as 20 miles w/o a problem by driving carefully and making sure the cake is on a *level* surface (like in the back of my SUV). Another consideration would be if the cake and vehicle were cold.
If the tiers are close in size - say 8,10,12 - you are asking for trouble and using a center dowel *might* help hold them together. Be sure to put a cake around that size on a BIG bottom board - even if it;s just for travel. The larger the base the better the 'tower' will ride.
When you say "skewers" I'm concerned you are not using dowels :( Again, it depends on the tier sizes but using plastic drink straws or wood dowels are necessary in general when putting 3 tiers together.
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