He swore oaths adjuring his children not to do certain things and the oaths were broken, but he has not offered expiation

It is makrooh to swear oaths too often, because Allah says (interpretation of the meaning): 

“And (O Muhammad) obey you not everyone Hallaaf Maheen (the one who swears much and is a liar or is worthless)”

[al-Qalam 68:10]

This condemnation implies that doing this is makrooh, as Ibn Qudaamah  (may Allah have mercy on him) said in al-Mughni 13/439. 

If you swore oaths upon your children or others with the intention that they should do something or not do something, and they went against your wishes, then you have to offer expiation for every vow that was broken, because Allah says (interpretation of the meaning): 

“Allah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masaakeen (poor persons), on a scale of the average of that with which you feed your own families, or clothe them or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your oaths (i.e. do not swear much). Thus Allah makes clear to you His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) that you may be grateful”

[al-Maa'idah 5:89]

If the oath was sworn repeatedly concerning a single matter, then you have to offer one expiation; if the oaths had to do with a variety of matters, then you have to offer the same number of expiations as the things concerning which the oaths were sworn. 

If you do not know for certain how many oaths were sworn, then try to figure out the number, and offer expiation until you think that you have most likely done what is required of you. 

The expiation for breaking an oath (kafaarat yameen) is mentioned in the verse quoted above: feeding ten poor persons with the average food that you give your own family, or clothing them, or freeing a slave. You can choose any of these three options. If you are unable to do any of these three things, then you should fast three days for each oath in question. 

The Standing Committee was asked the following question: 

In the past I used to swear oaths stating that I would do such and such, then I did not do it. I want to offer expiation for that. Is it sufficient to offer one expiation? Please note that I swore such oaths several times but I do not remember how many they were. 

They replied: 

Try to figure out the number of oaths that you have broken, then offer expiation based on that approximate number, if the oaths had to do with different matters. If they all had to do with the same matter, such as saying, By Allah I will not visit Zayd, by Allah I will not visit Zayd,” then offer one expiation. 

From Fatawa Islamiyyah, 3/481. 

Shaykh Ibn Baaz said: This applies to every vow to do one thing, or not to do one thing; even if it was repeated, only one expiation is due, provided that he did not offer expiation the first time and then repeat the mistake. But if he swore several vows to do different things or not to do different things, then he must offer expiation for each vow. For example, if he said: “By Allah I will not speak to So and so; by Allah I will not eat his food; by Allah I will not travel to such and such a place,” or he said, “By Allah I will certainly speak to So and so; by Allah I will certainly hit him,” and so on. 

What is required when feeding the poor in this case is to give each poor person half a saa’ of the local staple food, which is approximately one and a half kilograms. 

With regard to clothing, it means giving him what is needed for prayer, such as a shirt, or an izaar (lower garment, waist wrapper) and rida’ (upper garment, cloak). If he offers them dinner or lunch, that is good enough, because of the general meaning of the verse. 

From Fatawa Islamiyyah, 3/480 

And Allah knows best.