Sarah,
Your inquiry takes me back to childhood Scouting projects.
I agree with other postings, that it would be great to get some experienced assistance with this (for advice and authenticity at least), but if this isn't always available.
You don't specify what problems you are encountering. If your are doing this indoors, it may be with the anchoring and with the size of the dome you are attempting. 14' diameter is pretty large and would need several long, flexible support poles (willow or similar wood), each around 11' or longer. Wiki-ups are pretty basic structures, but most are dependent on solidly anchoring each main support pole into holes in the ground, or by wedging them against a heavy (and I mean heavy!) ring of rocks. Establishing the base is critical. All the other assembly is in bending and lashing lighter horizontal poles around the main posts to stabilize the structure; "filling in" the gaps with lighter branches; then finishing the exterior with your choice of water shedding material (overlapped "shingling" from bottom up with bundled long grass, inverted branches and leaves, sod, hide or blankets, etc.
If you can't really "anchor" your main posts into the ground, your engineering becomes considerably more complicated. Without a solid anchor for each post, the posts will want to kick out as you bend them, as your crew may have discovered. With good anchoring and strong flexible posts, a wiki-up should take less than a day to erect and finish, just as the Native American women did back when.
Paul