There are classical approaches using sequential extractions to separate calcite from FAP. Dolomite, unfortunately, behaves in acidic media more similar to FAP than calcite.
To avoid any contamiantion issues for the TEs (sequential extraction is seldom quantitative), and depending on the number of samples you have, you may think about the application of simple mixing model: Analyse the total TE content of Do-FAP mixtures (formed under the same conditions at one site) with different relative mixing mineral proportions (based phase analysis via XRD or total geochemistry) and estimate the composition of the end-members by extrapolation. Another approach would be La-ICPMS based.