1. Sorry about your discovery, dude. Warning, I caught my then-wife and it turned me into a private investigator of sorts...don't let the search for more evidence of the same thing become an obsession. You know she is cheating or planning to cheat, so the trust is broken. Don't confront her with it yet; at some point you should use it in negotiations because she is not going to want the word to be leaked into the public record. Protect your evidence.
2. Learn everything you can about state statutes for divorce, custody, child support, and property division. Read The List.
3. Decide whether the marriage is salvageable after the trust damage which has occurred. Janice Spring's "After the Affair" is a good book to guide you through reconciliation...and if reconciliation isn't the result (as in my case) it will help you process closure.
4. Obviously, change the locks on the house as soon as you can. ADT can probably replace the fobs as common as losing them must be, relegating the "stolen" one obsolete.
5. I can see how mention of the drugs and (at least) unauthorized entry raises the concern for your kids' safety. Have they mentioned anything unusual to you? Do you talk to them frequently enough to have a sense of a change in their demeanor during this time of your wife's emotional affair and intent to have extramarital sex?
6. Being a trashy wife does not equate to being a lousy parent unless she is exposing directly the children to danger, or having sex in front of them, or sharing/providing drugs to them. From what you've written, seems the label "unfit mother" would be a big stretch for the courts.
7. The kids are old enough that her sleep schedule is not an issue, unless there is a track record of truancy at school and poor grades. The court would rightly ask if this has been the case for 10+ years, why is it all of a sudden important. You have helped create a monster by allowing her to sit home on her fat crack while the kids were in school, when she could have gotten a job and help contribute financially to the household.
8. Become a student NOW of the things in point #2 above. Come back and ask questions along the way.
"Personal density is directly proportional to temporal bandwidth."