Firstly:  

Artificial insemination involves many things that are wrong. It has been proven that some doctors deliberately switch the sperm, either because they are evil themselves, or because they are certain that the man’s sperm is not fit for fertilization, and their greed for money leads them to do this. 

It has been proven that in many hospitals mistakes have been made and samples have been switched. Hence the scholars’ view on this matter is strict and they have stated that it is not permissible if the samples are stored and inserted into the woman’s uterus at a later date. Others have said that it is not allowed at all, because of the inherent dangers of error in this method which may lead to mingling of lineages and many other evils. 

Secondly: 

This insemination is not a case of necessity whereby a man and his wife may break their fast. It can be delayed until night or until after Ramadaan. 

What we advise you to do is to be patient and accept the decree of Allaah, and to apply the shar’i means of producing offspring. If you insist on artificial insemination then you have to take the strictest precautions to keep an eye on the sample and ensure that it is inserted immediately in your wife’s uterus by a female doctor whose religious commitment is trustworthy. And you should avoid doing this during the day in Ramadaan because there is no urgency. 

And Allaah knows best.