If there is any prohibitions against Intrauterine Insemination procedures for couples who is trying to increase their chances to conceive? If such trials not working against the G-D’s will, as soon as the key of procreation in Hashem’s hands and such procedures looks like trial to force G-D violently to make it happen? Appreciate your time and attention.
There is no prohibition against methods of artificial insemination (or intrauterine insemination). If G-d has allowed these techniques to come to our hands, then perhaps it is His will that we should use them for our benefit — and what greater benefit, for us, for klal yisrael, and for Hakadosh Baruch Hu, than begetting children.
We cannot know the Divine plans for us, and in general our guidance is from the laws of the Torah, though we can also draw guidance and direction from personal circumstances.
If no prohibition is involved (poskim discuss the issue of taking a sperm sample from the husband), it is permitted, and also the common custom, to increase chances of bearing children by means of intrauterine insemination.