First of all we have a couple of circumstances that may afford a verdict (fatwa) of a specialist as your wife has taken medicine to stop her period for the time of your 'Umrah, the impact of this on her health and the functions of her body can only be consulted with a physician and the fiqh related matters with a scholar who is able and well-versed to give fatwa.
This answer only gives a kind of guideline for what I'd call a usual case!
Allahs order on menses is clear:
And they ask you about menstruation. Say, "It is harm, so keep away from wives during menstruation. And do not approach them until they are pure. And when they have purified themselves, then come to them from where Allah has ordained for you. Indeed, Allah loves those who are constantly repentant and loves those who purify themselves." (2:222)
we are not allowed to approach (have intercourse with) our wives while they are in menses.
Scholars have three kinds of opinions on the duration of the menses one kind which is giving a limitation for the minimum and maximum days of menses, another that gives only a maximum day and a third that says there's neither of both which seems to be the safest.
As for the maximum a majority of scholars says it is 15 (full) days their major evidence for that is only the usually case and a very weak narration saying that woman spent up to half their life not praying (referring to menses). So there's no (good) backup for this neither in the Qur'an nor the sunnah, but a kind of good approach based on life experience.
Nevertheless those who consider a maximum of days say that any day longer is considered as isthadah and no more as menses however scholars have some good descriptions of both the "evidence" for the end of the menses (sse for example in al-Muwatta') and one could make a distinction between menses and isthadah based on:
Colour: menstrual blood is black [dark red] whilst the blood of istihaadah is red.
Consistency: menstrual blood is thick and heavy, whilst the blood of istihaadah is thin.
Smell: menstrual blood has an offensive odour whilst the blood of istihaadah does not, because it comes from an ordinary vein.
Clotting: menstrual blood does not clot when it comes out of the body whilst the blood of istihaadah does clot because it comes from a vein.
a woman can know that her period has ended by two things:
The white discharge which comes from the womb to show that the period is over.
Complete dryness, if a woman does not have this white discharge. In this case she can find out if her period has ended by inserting a piece of white cotton or something similar into the place where the blood comes from; if it comes out clean, then her period is over and she has to do ghusl and pray. If the cloth comes out red, yellow or brown, she should not pray.
(Source: islamqa #5595)
So in case of menses a woman is not allowed to pray while a woman having isthadah can or is allowed to pray and must perform wudu' for each prayer as long as she sees the blood.
Now as for having intercourse with a woman having isthadah there are two major opinions one of them is held by 'Aishah and some scholars like ibn Sireen, al-Zuhri, Ibrahim an-Nukha'i and others and one of two opinions of imam Ahmad. They say the blood of isthadah is harm as it is the case for menses therefore intercourse is prohibited.
The four imams and many other scholars nevertheless say it is permissible as the prophet () says:
... Not at all, for that is only a vein, and is not a menstruation... (see for example in sahih Muslim and sahih al-Bukhari)
which makes a clear distinction between both and worship in Islam has a higher rank than intercourse so if prayer is allowed intercourse should also be.
This is not 100% answering your question, but might hopefully help!
Some more fatwas on the topic:
islamweb #2278 (Arabic only)
islamweb #96616 (Arabic only)