Mechanical sex life, fights in marriage, staying together due to children. Recently attached to a girl not able to forget!

Any relationship requires the effort and consent of two people. Although you and your wife agreed mutually to marry, there are a lot of factors that go into the building of intimacy and love between a couple. Your wife seemed disinterested in sex from the beginning of your marriage. There could be various reasons for this- often women who are raised in strongly conservative families are taught to shun sex and their sexuality for a long time or till when they're married. Some women even after marriage have troubling embracing the idea of pleasure for themselves because they're told it's most about satisfying the man. And for the others, by the time marriage comes around, the idea that "sex is a bad thing" has engraved itself in their minds and they find it very challenging to embrace it and enjoy it. This is one possibility, others may also be involved.

Try initiating a genuine conversation with your wife about why she has abstained from initiating intimacy with you. Focus the conversation on why she hasn't involved herself and not on the absence of intimacy and pleasure for you.

Having a child early in a marriage does cut short the time to bond as husband and wife but does not necessarily curb it. Becoming parents twice should have also brought you both closer in some ways. Again, explore your wife's lack on involvement in the marriage, ask if you have failed to provide something for her comfort- emotionally, mentally and physically. Sometimes just asking the right questions is enough to open a channel of communication.

Addressing one other statement; staying in a loveless marriage for children is potentially more harmfully than separating. Your children will eventually make peace with your decisions should choose to make them with sensibility and civility. It will be different and strange for sometime but they will adapt and understand to any change their parents go through as long as it's properly explained to them and properly executed for them.

Lastly, about the woman you met online, if you are certain you want to work on your marriage first before considering anything else, I would suggest that you cut off contact from this girl and focus only on your marriage. Abstaining from keeping in touch or acting on your impulse to go ahead with this girl is the only way you can full focus on your marriage. Based on how things go forward with your wife, should you choose to call it quits on your marriage, then you can move on from the relationship into a new one where hopefully your feelings and needs are reciprocated.
Indulging in something while your still married can be a messy affair and also brings in the aspect of morality. Consider these things before you make a choice in either direction.