I can't tell you not to worry about your kids. I see red flags going up every which way in this sitch.
Is it normal. YUP, this is what someone in MLC who wants to be footloose and fancy free does to relive what she thinks she missed does.
You really should talk to your ex first. Give her fair warning of your intentions and your concerns. Lay down the law and tell her that this is what you expect in no uncertain terms. Your kids are you first concern as they should be. If anything ever happened to them you would never forgive yourself. If she doesn't make some changes I would consult an attorney. You know it wouldn't hurt to go ahead and get a consult one just to see what your rights and options are. I hate to tell you this but I don't think that your talking to her will be the quick fix that you're hoping for.