It's reasonable for a woman to lie about her past ****tyness to her prospective husband. My view is you do no good whatsoever dragging this information out of her. She is the mother of your children. You chose her. If all of this stuff was so important to you you had every opportunity in the 6 years prior to chidrren to find out everything you needed to know. You didn't do it. You now have kids, who need a family, the past is long over so you should live in the present. You must conquer your insecurity..
Maybe its common for a woman to lie about her past, but I don't think it is reasonable. When we go through the decision process as to whether to pursue a relationship, we decide based on what we know about her. At the time, if the OP knew that she had slept with these common friends, but chose to make him believe that she didn't ... well, she'll obviously lie if its convenient. That's a fact that might raise a few red flags. Who cares about the past, I know, but this happened while he was with her. Lettermen might even put it in his top ten list as great ways to humiliate a guy.
In one respect, the OP has conveyed what he fears to be a critical flaw in their relationship. I think he fears that the harsh reality is that trust is probably not something that he should bank on, at a minimum, going forward. He's afraid that he is going to hear exactly what he needs to hear from her to keep things running smoothly. Trust will be something that she doles out on her own terms.
Personally, I think its okay to choose to toss aside the politically correct assumptions that make us feel mature, sophisticated, and accepting. Or at least but them in the proper cubbyhole, and deal with the underlying issue that the OP is needing to explore. There is nothing refined, or sophisticated about trust. Its gained in stark, black and white terms. You have it or you don't, unless you are a paranoid individual. Lay it on the table, but tell her that you want to be able to leave the past in the past. It doesn't have to matter going forward, but trust does matter. Does she consider it appropriate to avoid telling him things that might make him feel ashamed if he knew, while they were together as a couple? Did she assume that the unrevealed medical procedures would have no impact on their ability to have children in the future? Can he trust her not to pursue future emotional and possibly sexual relationships when she uses social media?
And, contrary to popular opinion, cheating doesn't imply a fixed connection to a husband or wife not meeting the needs of a cheater. Its an optional pattern that is sometimes involved. Some people just enjoy the pursuit of new lust. Others just find it easier than working to fix the problems. Marriage is about mutual responsiblity, and not a person's responsibility to keep another from cheating.