There is some preference to scheduling insemination for after mikveh. However, insemination prior to immersion is widely considered to be halachically permissible.
Insemination is generally timed in coordination with a woman’s ovulation. You don’t specify whether you plan to use a trigger or natural ovulation, which could affect this planning. Please consult your physician about your medical options, and also about optimal timing of relations once the IUI is set.
If treatment does take place on Friday, then it does not delay immersion as long as you perform a bedikah that day before the procedure. (Insemination before day seven could entail a delay.) Relations may be delayed to after mikveh night by a day or two if that will help maximize chances to conceive.
Please let us know if we can be of further assistance. You may also find it helpful to arrange a free consultation with a Yoetzet Halacha Fertility Counselor, details here.
This response was updated on 3 May, 2021.