Thank you for reaching out to us!
Ashkenazi practice is to recite the bracha between the first and second dip. This accomplishes two goals. First, it enables the bracha to be after immersion, keeping the order consistent with how the bracha must be recited for a convert, who cannot recite a bracha before immersing. Second, it enables a bracha to be recited right before mitzva fulfillment in the second dip, consistent with the usual order of brachot and mitzva acts.
Reciting the Yehi ratzon is not obligatory, and we would ideally not want it to interrupt between the bracha and the second dip.
Therefore, we recommend reciting the Yehi ratzon either after the second dip or after the final dip, as a sort of capstone to the immersion process. A woman’s immersion practice typically follows her mother’s customs. So, if relevant, we would also suggest checking in with your mother and adopting whichever of these options most closely aligns with her practice.
Please let us know if we can be of further assistance.