Firstly: 

It should be understood that intercourse during the day in Ramadan, for one who is fasting and is staying at home (i.e., not travelling), is a grave sin and what one must do is repent from it by praying a great deal for forgiveness, regretting it, acknowledging that it is a sin, and feeling sad for having done it. One should also do a lot of acts of obedience and worship, and resolve not to go back to that sin. In addition to that, there are five consequences: 

1.Incurring sin

2.rendering the fast invalid

3.obligation to refrain from eating and drinking for the rest of the day

4.obligation to make up the day when the fast was broken

5.obligation of offering expiation (kafaarah) 

In this case the expiation is severe: it is to free a slave; if that is not possible, then one must fast for two consecutive months; if he is not able to do that, then he must feed sixty poor persons. 

It makes no difference whether ejaculation occurred or not, so long as intercourse took place. 

That is different from the case if ejaculation occurred without intercourse; in that case no expiation is required, but one still incurs sin, must refrain from eating and drinking for the rest of the day, and must make up that fast. 

Please see the answer to question no. 22938 and 148163 

With regard to what it says in the question, “he ejaculated before doing the intercourse”, if his penis entered his wife’s vagina, even if that was after ejaculation had occurred outside, then the severe expiation must also be offered in this case, because intercourse took place. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (35/55): 

There is no difference of opinion among the fuqaha’ concerning the fact that expiation must be offered by anyone who has intercourse in the vagina during the day in Ramadan, deliberately and with no excuse, whether he ejaculates or not. End quote. 

In that case, the husband must offer expiation for every day on which he had intercourse. If intercourse occurred on the second occasion, then he must offer expiation twice. 

Please see the answer to question no. 12329 

If it was merely foreplay or thinking about intercourse, then when he ejaculated he felt lethargic and could not penetrate the vagina, then undoubtedly he was sinning by doing that, and he transgressed the limits set by Allah; he must repent, as must his wife if she took part willingly, but they only have to make up the day on which they broke the fast. 

Secondly: 

If a person is aware that intercourse during the day in Ramadan is haraam, but he does not know that expiation is required for it, he must still offer expiation, because ignorance of the punishment is no excuse. 

Please see the answer to question no. 21806 

Thirdly: 

The expiation for intercourse during the day in Ramadan is one of three things, in this particular order. It is not the matter of choice, i.e., it is not permissible to move from one to another unless one is unable to do what is stipulated. They are: freeing a slave; if one cannot do that, then one must fast for two consecutive months; if he cannot do that, then he must feed sixty poor persons. It is not permissible for him to fast for two months if he can free a slave, and it is not permissible for him to feed sixty poor persons unless he is unable to do the first two actions, freeing a slave or fasting. 

The scholars of the Committee said: 

Expiation for intercourse during the day in Ramadan is done by doing one of the things mentioned above, in order of preference. One cannot move to fasting, for example, unless one is unable to free a slave; and one cannot move to feeding the poor unless one is unable to fast. If a person moves to feeding the poor because he is unable to free a slave or fast, it is permissible for him to offer iftaar to sixty poor or needy persons who are fasting, giving them enough to eat their fill of the local staple food, once on his own account and once on behalf of his wife. Or he may give to 60 poor persons sixty saa‘s on his own behalf and on behalf of his wife, giving each one a saa‘, which is equivalent to approximately 3 kg.

End quote from Fataawa al-Lajnah ad-Daa’imah (9/245) 

Please see also the answers to questions no. 93109 and 106533 

If the one who is obliged to offer this expiation has to feed the poor (because he is unable to do either of the first two actions listed), then there is nothing wrong with him delegating a trustworthy charitable organisation to feed the poor on his behalf, or distribute this food on his behalf to the poor. 

You can also delegate your husband to offer the expiation on your behalf. 

There is nothing wrong with sending the expiation to your original homeland, if the need there is greater because of the large numbers of poor people, as this may serve a greater purpose. 

Ibn Muflih (may Allah have mercy on him) said: 

It is permissible to transfer vows, expiation and bequests, according to the more correct scholarly opinion.

End quote from al-Furoo‘ (4/265). 

There is also no reason why your husband should not give this expiation on your behalf, if you consent to that. 

Fourthly: 

If a man has intercourse with his wife during the day in Ramadan, one of two scenarios must be the case: 

1.That at the time of intercourse the woman was excused because she was forced, or she forgot, or she was unaware of the prohibition on having intercourse during the day in Ramadan. In that case her fast is valid, and she does not have to make it up or offer expiation.

2.That she had no excuse; rather she willingly obeyed her husband in having intercourse. There is a difference of opinion among the scholars as to whether she is obliged to offer expiation in this case. The more correct view is that she is obliged to offer expiation in this case just as her husband is.

Please see the answer to question no. 106532 

Fifthly: 

If the woman is obliged to fast for two consecutive months, and she starts to fast but then her menses comes, then that does not interrupt the sequence of her fasting. She should stop fasting (for the duration of her period), then make up the day’ missed whilst she was menstruating, and then complete the two months. 

The same applies if she starts to fast then ‘Eid comes. She should stop fasting on the day of ‘Eid, then resume fasting immediately afterwards. Breaking the fast on the day of Eid does not interrupt the sequence of fasts in the case of a fast offered as expiation. 

Please see the answers to questions no. 82394 and 124817

Sixthly: 

If a woman breaks her fast by having intercourse or otherwise, then she gets her menses a few hours after breaking the fast, the excuse of menses does not mean that the obligation to make up that day or offer expiation is waived, because she incurred the sin before the excuse came into effect; in other words, she did the forbidden action with no excuse, so the excuse does not have any impact on the ruling, just as it does not waive the burden of sin. 

And Allah knows best.