I’m not sure I understand the problem and without knowing how to do it in mother, but:
if you have a tree where each representative sequence corresponds to one tip, it is (almost) always the case that the same sequences are found in different samples. Otherwise each sample would have a complete unique OTU composition. AFAIK, uni-frac explicitly quantifies the fraction of shared (uni) branch length, and weighted unifrac simply weights the branches by the abundance of the OTU at the corresponding tips.
In R, you can compute the unifrac distance easily with the phyloseq package (Picante has it too but not weighted and much slower):
OTU: your OTU table
ID: Your metadata table with sample names as rownames, corresponding to sample names in OTU table
TREE: your phylogenetic tree, with tip labels corresponding to OTU names in OTU table