Problems are problems, it doesn't matter if it is a divorce proceeding or something else. I'm glad you are reaching out for some help and advice here. You need to do it in real life too.
Time for a reality check...
Illegal Alien, the time for you to STOP being naive and trusting in the goodwill, good "word" and reliability of your Ex wife and anyone associated with her is right NOW. You need to get professional legal advice immediately, both where you are living now and in Mexico. I would start with any free legal aide services or referrals you can find where you are living now.
Explain the situation in full, honestly and do not leave out any details. It might help you to write up a brief overview of the entire marriage, separation and divorce, with a timeline, to help you tell it precisely. Be sure to explain that you were in a Cult which requires members to divorce one another when one is no longer in good standing. Don't be afraid to explain about Scientology's Sea Org and how they recruit young teenaged children of their loyal Cult members to serve billion year contracts, and your concern for their welfare.
You will also have to get a Mexican attorney to assist you, at least with filing paperwork with the case there, if not actively represent you. Hopefully, if you find an attorney where you live, they may be able to refer you to one in Mexico.
Knowing these additional details, DO NOT go to Mexico yourself until you have independently assured yourself that the non-support charges and fines against you have been resolved, or you may find yourself jailed for non-payment of child support. Take this very seriously. This may be the real reason why your Ex wife is suing you over this non issue, which you had worked out in verbal agreement with her, but technically is correct and is being used against you.
Usually the matter of support, custody and visitation is clarified and spelled out in the divorce documents. You need to get your hands on true copies of all the legal paperwork involved to take to your attorney. Do not rely on any paperwork which your Ex wife has sent you, as it may have been altered or be incomplete.
It is possible that you were never notified about this second action against you because your wife told the court that you had abandoned them after stealing money from the family firm for years, and she did not know of your whereabouts. She seems to have lined up some kind of paperwork to be able to make this claim against you, with assistance from Scientologists, whether forged or not. Remember that manufacturing evidence against you to ruin you utterly is in keeping with the COS directives on the treatment of SP's.
It seems she has also (perhaps at the prompting of her attorney) manufactured threats by you against her life and the children's to strengthen her case for custody and non visitation. If these claims against you are untrue (and I believe they are) you need to carefully do a record check for where she lives in Mexico to see if she has taken out anything like a restraining order or order of protection against you, so she can have you arrested if you come near her or the children. It's a little disingenuous of her to tell you that you can come to visit the kids in Mexico anytime, when she is suing you for non payment of child support, isn't it? So I would suspect that she has set some kind of a legal trap for you. Maybe this hasn't happened, but you don't want to be blindsided by anything like this, if it has.
Do not trust her or rely on anything that she says, about the children or anything else. Verify everything yourself. Do you have any loyal friends left in Mexico who might help you to do legal research or insure the children's wellbeing? Not her friends or family, but yours. Obviously, not Scientologists! If so, contact them.
You already knew she was a financial cheat, now you know she is a lier and blackmailer as well. This tells me that you are basically dealing with a criminal mindset here, who will do or say anything to get what she wants. Please get some professional legal advice NOW and do not try to "work out" any negotiation with her on your own.
What I have said may seem harsh and shocking, but I mean it to be a reality check for you. Being stuck in a Mexican prison on manufactured evidence and testimony would also be harsh and shocking.
You will have to be able to prove that she was the major income earner, and that most of it was off the books and under the table, no taxes paid. This might be very hard to do from a distance, but a good attorney there with a PI could likely dig up some evidence of large expenditures she has made or testimony about this hidden income to the business.
I wouldn't worry about starting a war with your ex-wife, or her trying to poison the well of your children's attitude about you. You've already been in a war with her all along, over custody of your children, her freedom and illegally kept earnings, you just didn't realize it. Chances are good that she has already positioned you as the bad guy in the divorce, and your leaving Scientology, and told them or hinted at whatever slander she it trying to hold over your head.
Do I have to say that at this point you should not believe a word your wife says? Do not think that you can reason with her or get into an agreement that will stand. She has stacked the deck in her favor in every way.
Here in California, when a divorce proceeding is terribly one sided and hugely benefits one party over another, often that party can go back to court and argue for a "do-over", to change the terms of the divorce. Something similar may be possible in Mexico. You will have to do a bit of research about divorce laws in Mexico. You can say you were so shattered about the Scientology declare and pending divorce that you were not thinking straight or acting in your own best interests.
If you did sign for the kids to get their passports, be prepared that they maybe soon be out of the country, on the Freewinds or elsewhere, and may end up in a Scientology Cadet school or the Sea Org, without your being notified of it or told of their location. She wanted their passports for a reason. This would be a good motivator for you to find a friend in Mexico who can give you reports on the children's well-being and whereabouts independent of what your Ex wife is telling you. Possibly contact their school yourself, ask for their grades and quarterly reports, etc.?
Good luck to you. Keep us informed as to how things are going. Stay safe.
One other thought...if you recorded your Mexican marriage in some other country, you may still be legally married in that country. That is the case here in California. So you may still have some legal rights and recourses outside of Mexico, if this is the case. Good luck.