@Anonymouse123, there are two possibilities here. It's either the beginning of an emotional relationship at this stage or she is just looking for attention to feel attractive. After having two kids, there is a good chance of the latter.
Emotional attachments are a lot more dangerous to your marriage than a pure sexual relationship imo. There are ways to fix a marriage if there are sexual issues if both parties are open, but if you are detached and not doing well on an emotional level, it can be quite difficult in mending things.
I suggest you don't beat about this bush and confront this ASAP. Don't be confrontational, or angry when you approach her. Sit her down away from the kids and other distractions and tell her what you have found. Tell her you are heartbroken, but love her, and your life together and you want to understand why this is happening, and work on a way to fix things.
She is going to lash out at you. She is going to be embarrassed, feel like her privacy has been invaded, and make up all sorts of excuses. You just need to be firm (don't escalate, because it can turn ugly really quickly). Ask that she cut off all contact so you can move on over this bump together. It's going to be a bit of a process, but cool heads and open communication will prevail.
Without understanding the underlying issues in your marriage, or your wife, it's really hard to give any other advise. It sucks. Must have felt like being punched in the stomach when you saw those messages. She could just be feeling like she needs attention (all women do at different times of their lives).