Question Summary:
Can a woman in her post-marital waiting period [‘idda] take medicine to hasten the end of her ‘idda?

Question Detail:

 
is it permissible for a women in iddath to take tablets for her to come out of iddath in 3 weeks

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
The wisdoms of the post-marital waiting period ['idda] are an indication of how sacred the institution of marriage [nikah] is in Islam:
→ It gives the husband (when the divorce given is revocable) the ability to reconsider his decision and hopefully lead to reconciliation rather than a dissolution of marriage. 
→ In the case of an irrevocable divorce when the husband and wife can still re-marry, it again allows sufficient time for the couple to reconsider and see if they can give it a second chance together by re-marrying instead of going their separate ways.
→ It is a means of preserving the lineage and clearly discerning if the woman is pregnant so that the child's lineage is known without any ambiguity or doubt. 
Taking the above into consideration, it would be best not to take the medicine in order to hasten the end of the post-marital waiting period. 
However, if the medicine taken is halal and does not adversely affect the health of the woman, then, yes it will be permissible to take this medicine. [i][ii]
Keep in mind that the 'idda of divorce or khul' is three complete menstrual periods with a minimum of 15 days (360 hours) or more of purity [tuhr] between each menstrual period. 
Therefore, the 'idda will end with the completion of the 3^rd menstrual period after divorce.
(Note: If she was divorced during a menstrual period then that menstrual period will not be considered and will not count towards fulfilling her 'idda).
And Allah Ta’āla Knows Best 
Mufti Sohail ibn Arif,
Assistant Mufti, Darul Iftaa
Chicago, USA
Checked and Approved by,
Mufti Ebrahim Desai.
وعليه فالمرضع التي لا ترى الدم في مدة إرضاعها، لا تنقضي عدتها إلا بالحيض كما سيأتي التصريح به في [i]
باب العدة  وقال في السراج: سئل بعض المشايخ عن المرضعة إذا لم تر حيضا فعالجته حتى رأت صفرة وقال في
السراج: سئل بعض المشايخ عن المرضعة إذا لم تر حيضا فعالجته حتى رأت صفرة في أيام الحيض قال: هو حيض تنقضي به العدة. اهـ
 رد المحتار، ١/ ٣٠٥ 

وعليه فالمرضع التي لا ترى الدم في مدة إرضاعها، لا تنقضي عدتها إلا بالحيض كما في الدر من باب العدة [ii]
وفي السراج سئل بعض المشايخ عن المرضعة إذا لم تر حيضا فعالجته حتى رأت صفرة في أيام الحيض قال: هو
حيض تنقضي به العدة
مجموعة رسائل ابن عابدين ١/ ٨٣