It is highly recommended for women and children to accompany their spouses and fathers to the masjid for the Eid Prayer. The prophet (peace be upon him) used to encourage his companions to bring their whole family for this prayer. Nevertheless, back in our prophets era women used to dress much more modestly and adhered to the sunnah sometimes even more strictly than the male companions themselves.
Briefly after the death of our beloved Prophet (p.b.u.h.) women started to change, dressing more provocatively and mingling with men in the streets and markets. For this reason, Omar may Allaah be pleased with him, enraged by this kicked the women out of the masjid and when they complained to Aisha (our Prophets wife) she justified it saying that the women who used to come to the prophets masjid were very different from those Omar banned from the masjid.
In this occasion of Eid I feel the need to share my own observations and advise new Muslims about what to expect at the masjid when they arrive for Eid. It can often be overwhelming the first time you enter a masjid during Eid. It is not uncommon to walk into a masjid during Eid and find women decked out in jewelry, gold, bright colored outfits, transparent clothing and tiny hijabs which barely cover their hair and leaves little to imagination. They are often decked out in high heels, hair done and styled, faces painted up, nails polished, etc.
It is also not uncommon to find these same women chatting during the Eid Lecture. For Eid it is the sunnah to wear something new, however a woman's beauty should be kept for her mahrams especially her spouse. Other sunnahs include taking a shower before coming for prayer. Often after the prayer women and men join one another outside and chitchat.
This behavior is not allowed and should be avoided. The mingling of sexes increases fitnah. Needless to say, the display of jewelry and gold hurts the feelings of the less economically favored sisters and makes them feel inferior which is in direct opposition of the sunnah of the prophet (peace be upon him) and the basics of sisterhood.
With that said, please don't take offense to the sisters who ignore you and look down on you for not dressing like them and following their cultural behaviors. On the contrary we should make duas and supplications that Allah (swt) guides their hearts and purifies their intentions.