The reward for women going to offer Eid Prayer is the same as that of men. The Qur’ān says:
“And whoever does good deeds whether male or female and he (or she) is a believer- these shall enter the garden, and they shall not be dealt with a jot unjustly.” (Q. 4:124)
However, it is not necessary for women to participate in the Eid Prayer. About participating in congregational Prayer (that also applies to Eid Prayer) Mr. Ghamidi writes:
“Women, however, are exempted from this directive. For them the sunnah is that they can come to the mosque for the Prayer but the Prayer offered at home is better for them. The Prophet (sws) is reported to have said: "Do not stop your women from coming to the mosque, but they should know that it is more appropriate for them to pray at home. (Abu Da'ūd, No: 567).
It can be derived that the main reason for the above mentioned preference is to make sure that, being a congregational Prayer (in particular in Eid times when usually it is more populated) the busy crowd does not put male and female in a situation where it might be difficult to observe appropriate ethical limits with regard to gender interaction.
This also guarantees that while one member of the family (father) is away, another adult member of the family (mother) is in charge at home to take care of kids and other family affairs.
Obviously depending on circumstances that may affect the above mentioned issues, individuals (among women) need to determine whether it is better for them to stay at home or to attend congregational Prayers including Eid Prayer.
The fact of the matter, however, remains the same, that is, attending Eid Prayer is not obligatory for women.
In principle, there is no harm in women going to graveyard as long as they make sure that emotional feelings will not cause them to go beyond the boundaries and ethics that are prescribed for a Muslim. To be specific, this means not to create scenes by screaming and extreme wailing.
There are of course Aḥādīth ascribed to the Prophet (sws) indicating that the Prophet (sws) forbade people, and in occasions, women in particular from visiting graves.
However, there are aḥādīth ascribed to the Prophet (sws) indicating that later on the Prophet (sws) allowed and in fact recommended people (including women) to visit graves.
It can be understood that at the beginning, because of some of the baseless and superstitious beliefs of Arabs about death and graves, the Prophet (sws) forbade the believers visiting graves. In particular in the case of women, it seems like there was an additional reason for this and that was the habit of women to go to extremes in crying and mourning when they were visiting graves.
Later when the foundations and values of Islam were reasonably settled in the society the Prophet (sws) allowed people in general to visit graves, in particular because visiting graves reminds people of death and the Hereafter.
Therefore, as long as one (man or woman) refrains from going to extremes in mourning (and of course as long as the person does not consider the grave to be a source of fulfilling Prayers) it is fully okay for one (man or women) to visit graves.
A relevant ḥadīth for your interest follows:
“‘Abdullāh b. Mulayka says: “‘Ā’ishah (rta) was coming from graveyard so I asked her: “O mother of the believers, where are you coming from?” She said: “From visiting the grave of my brother ‘Abd al-Raḥmān b. Abī Bakr.” I said to her: “Did not the Prophet (sws) forbid visitation of graves?" To this she replied: "Yes, he had forbidden it. Then he ordered to visit them”. (Al-Mustadrak No. 1392).
 Islamic Sharī‘ah of the Prayer, translatedbyShehzadSaleem.