She got her period twice in one month, and the two periods together added up to more than fifteen days
Question

My mother got her period, then she became pure after seven days, as usual, then one week later, she got her period again. Is this regarded as menses? Should she pray and fast? Please note that she takes measures to prevent that and she is approximately forty-eight years old. Should she continue not to pray throughout the two periods, even if they add up to more than fifteen days?
Praise be to Allah.The scholars (may Allah have mercy on them) differed regarding the minimum duration of the state of purity between two menses. We have stated previously that there is no minimum duration of the state of purity between two menses, so if a woman’s period comes to her after the previous period, then she is menstruating, whether the time between the two menses was long or short.
Please see the answers to questions no. 37828 and 20898 .
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
As for the minimum duration of the state of purity between two menses, it was said that the minimum is thirteen days, and it was said that there is no minimum, just as there is no maximum, and this view is the one that is correct.
Based on this correct view, it is possible for a woman to menstruate twice in one month, but the woman should know that menstrual blood is what is menses, whereas the other kind of blood, which is thin and yellowish, is not menses; rather it is irregular bleeding (Istihadah). (End quote from Fatawa Nur `ala Ad-Darb by Ibn `Uthaymin).
For more information, please see the answer to question no. 5595 .
Based on that, with regard to what happened to your mother after one week, if its characteristics were those of menstrual blood, then it was menses.
With regard to the two menses lasting beyond fifteen days in the case of one who menstruates twice in a month, that does not matter. There are some women who menstruate for sixteen or seventeen days of every month, and that is their normal, regular pattern.
Ibn Taymiyah (may Allah have mercy on him) said: There is no minimum or maximum duration (for menses). Rather what a woman sees as her normal, regular pattern is menses. If it so happens that it lasts for less than a day and that is her regular pattern, then it is menses. If it so happens that it lasts for seventeen days and that is her regular pattern, then it is menses.
But if the bleeding is continuous, then it is known that this is not menses, because it is known from Islamic teachings and from linguistic usage that a woman is sometimes pure (not menstruating) and is sometimes menstruating, so there are rulings for her period of purity and there are rulings for her menses. (End quote from Majmu` Al-Fatawa, 19/237)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
What is meant by “its maximum is fifteen days” is the maximum duration of menses. This is the view of the madhhab and they quoted as evidence what is typically the case; it is typically the case that a woman’s menses does not exceed fifteen days. Moreover, anything beyond this time would take up the greater part of the month, and it is not possible for the period of purity to be shorter than the duration of menses.
So if it is sixteen days, then the period of purity would be fourteen days, and it cannot be the case that the bleeding lasts for longer than the period of purity…
However, the correct view is that there is no maximum duration of menses, because there are women for whom the regular pattern is seventeen days, or sixteen days. What is it that makes the blood before sunset on the fifteenth day menses and the blood one minute after sunset irregular bleeding (Istihadah), even though the nature, colour and abundance of the flow are the same? So how can it be said that within the space of one or two minutes the blood turns from menses to irregular bleeding with no evidence? If there was any evidence to support what they say, we would accept it.
So if the woman has a normal, regular pattern of seventeen days, for example, we say that it is all menses.
But if the bleeding continues for the entire month, or it stops briefly, such as for a day or two, or it is intermittent, so it comes for a few hours and stops for a few hours throughout the month, then this is irregular bleeding (Istihadah).
(End quote from Ash-Sharh Al-Mumti`, 1/471-472).
And Allah knows best.