What if we live in Europe and there is no choice to do it with the wife’s hands because the man have to do this in the clinic here. And as a woman you are not allowed to go there too.

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If the insemination (having kids) is not vital for both of you, then it is not permissible, neither in Ramadan, nor in other months.

There are two points here:
1- You will do the Masturbation with your own hand, which is haram.
2- You will practice in front of other people, which is also haram.

Can not you ask them to give you a container, where you can pour the semen in at home, and take it to them immediately?