All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The Friday prayer is an obligation upon men but not upon women and what you mentioned that you have children is not a sound reason for not attending the Friday prayer as millions of Muslims have double the number of children that you have but this does not prevent them from performing the Friday prayer.
If a child sleeps in a separate room, then you should not be afraid that he may harm himself as long as the place where he is, is safe. Even if your two children wake up and start crying, then this does not matter and it is normal for children to cry at the same time, as the mothers are usually experienced in dealing with the children in such cases.
Since you leave your two children with your wife when you go to work, then you should leave them with her when you go to the Friday prayer. So, dear brother, you should fear Allaah and know that not attending the Friday prayer without a sound reason is a grave major sin and it is a reason for having one’s heart sealed; we seek refuge in Allaah from this.
Indeed, the Prophet said: “People must stop neglecting the Friday prayers otherwise Allaah will seal their hearts and thus they will be among the heedless.” [Muslim]
Besides, Abul-Ja’d Adh-Dhamri who is considered to be among the Companions of the Prophet narrated that the Prophet said: “Whoever misses three Friday prayers (consecutively) out of negligence, Allaah will seal his heart.” [Ahmad, Abu Daawood, Ibn Maajah, At-Tirmithi and An-Nasaa’i]
For more benefit, please refer to Fataawa 91358, 138018 and 124673.
Allaah Knows best.