I would attempt to communicate a similar message as the one suggested by frission, but do it in a less confrontational manner.
I recommend talking to a counselor because they can help you navigate the complicated emotions she's experiencing without putting her on the defensive.
If you think you're skillful enough to negotiate those rocky shoals then I would recommend the following:
Genuinely ask her why she wants to re-establish the relationships. It is possible the finality of death and the finite and fragile moments of life hit her strongly at the funeral. And she realized that despite the horrible things that have happened in the past, these people did feed, clothe, and care for her until adulthood. Perhaps she feels a longing to develop the love and affection which you have enjoyed from your family.
If she trust you enough to truly explain why she want to do this you're golden; if you don't screw things up. To screw things up you only need to say, "it won't work," or "they are bad people," or some other thing which fails to recognize and validate her desire to build the relationship.
A better way would be to say, "I think I understand, you want to ... [restate what you thought you heard]." If she says yes, then you could say something like, "I can see how this is important to you and I want to support you, but I have some concerns because of some of the things which have happened in the past." At this point you would voice your concerns using shared experiences in which they screwed with you, her, and your family. You would voice your concerns regarding the potential for them to jeopardize your marriage again. Then you would voice your concerns how their interaction might affect your kids.
Then you would ask her if there is a way that you to can figure out how she can "Test the waters" without exposing the family to problems similar to those experienced in the past. Perhaps it is a casual monthly or bi-weekly phone call and that she promises to politely but firmly hang up if they start to talk disrespectfully about you, her, your family, etc. If the in-laws are not receptive, she can simply stop calling them. If they are receptive and respectful she might meet them for coffee after a couple months.
The most important thing for you to communicate is your commitment to her, her welfare, and the welfare of your children. With this loving support based upon the precepts of protecting your family, she may be able to determine whether or not the effort is a lost cause before serious damage can occur. If you fail to recognize and support her in her effort to reach out, you may push her towards the very thing you want her to avoid.
Good luck.