The pregnant woman is obliged to pray like any other woman who is in a state of purity. Prayer is only waived for women in the case of menses or nifaas (postpartum bleeding). Knowledge of that is widespread and readily available, and ignorance of that is very strange, especially in Muslim countries. Rather it is to be regarded as a shortcoming and negligence.
What every accountable individual must do is learn what he needs for his acts of worship and interactions with others to be sound and valid. This is part of the knowledge that it is obligatory to acquire, and it is not permissible to delay it or be distracted from it.
Therefore what your wife must do is repent to Allah, may He be exalted, for her shortcomings and negligence in learning and asking people of knowledge. But she does not have to make up these prayers, according to the more correct scholarly opinion, regardless of whether she did not do them out of ignorance or heedlessness, but she should strive to do a lot of acts of worship and obedience, and a lot of naafil (supererogatory) prayers.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
Based on that, if a person does not purify himself as he is obliged to because the text did not reach him, such as if he eats camel meat and does not do wudoo’ after that, then the text reaches him and it becomes clear to him that wudoo’ is required in this case, or he prays in the camel pens, then the text reaches him and the ruling becomes clear to him, does he have to repeat his past prayers? There are two scholarly opinions, both of which were narrated from Ahmad.
A similar case is if he touches his penis then prays, then it becomes clear to him that it is obligatory to do wudoo’ after touching one’s penis.
The correct view in all these cases is that he does not have to repeat the prayers, because Allah pardons things done by mistake or because of forgetting, and because He says (interpretation of the meaning): “And We never punish until We have sent a Messenger (to give warning)” [al-Isra’ 17:15].
If the command of the Messenger (blessings and peace of Allah be upon him) concerning a particular matter did not reach a person, then the ruling that it is obligatory was not proven in his case. Hence in the case of ‘Umar and ‘Ammaar, when they became junub and ‘Umar did not pray whilst ‘Ammaar did pray after rolling in the dust, the Prophet (blessings and peace of Allah be upon him) did not instruct either of them to repeat the prayer. Similarly, he did not instruct Abu Dharr to repeat the prayer when he used to become junub and remained for several days without praying. And he did not instruct the Companion who ate until he could clearly distinguish the white thread from the black thread to make up the fast. And he did not instruct those who prayed facing towards Jerusalem before news reached them that this ruling (of facing Jerusalem when praying) had been abrogated to make up those prayers.
A similar case is that of the woman who was suffering from istihaadah (irregular, non-menstrual bleeding) and did not pray for a while because she thought that prayer was not obligatory in her case. There are two scholarly views as to whether she is obliged to make up the prayers. The first view is that she is not required to do so – as was narrated from Maalik and others – because when the woman who was suffering from istihaadah said to the Prophet (blessings and peace of Allah be upon him): I bleed very heavily and that has kept me from praying and fasting, he told her what she had to do in the future, but he did not instruct her to make up prayers from the past.
It is proven to me through the mutawaatir reports that among women and men in the desert and elsewhere there are those who reach the age of puberty and are not aware that prayer is obligatory for them. In fact, if a woman is told to pray, she says, Not until I am older and become an old woman! – thinking that prayer is only obligatory for old women and the like. Among the followers of the shaykhs (i.e., Sufis) there are many groups who do not know that prayer is obligatory for them. In these cases they are not required to make up the missed prayers, according to the correct opinion. End quote.
Majmoo‘ al-Fataawa (21/101, 102)
Nifaas is the bleeding that occurs with childbirth, or two or three days before childbirth, if it is accompanied by signs of impending childbirth, such as contractions.
It says in Kashshaaf al-Qinaa‘ (1/219):
If she sees blood three days or less before any part of the child emerges, and she feels pain, then this is nifaas, like that which appears with childbirth. End quote.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about a pregnant woman: a few days before she gives birth she experiences bleeding and the like; when does prayer become waived in her case?
The scholars say that nifaas is the blood which appears at the time of childbirth, accompanied by contractions. If the contractions come one or two days before the birth, then this is nifaas. As for bleeding which occurs without contractions, it is not nifaas, even if that occurs on the day that she gives birth. When the bleeding of nifaas stops, some time after giving birth, then when she becomes pure she must purify herself (ghusl) and start to pray, and she should not wait for that time to be completed.
End quote from al-Baab al-Maftooh (no. 31/8).
If a woman is about to give birth and she feels labour pains and starts to bleed, then that is the blood of nifaas, and she should stop praying and fasting.
But if no blood appears, she should pray even if the cervix has started to dilate, and she should carry on praying until she gives birth.
And Allah knows best.