I understand your feelings - I have worked in RCIA for about 25 years, and marriage issues tend to be one of the likeliest to arouse anger.
When you refer to “join another” I would hope that you are referring to another parish, not some non-Catholic church.
No one - and I mean no one - can say your children are not legitimate; the Church does not say that and neither does the State (at least, in the US). The people who are working with you are not saying you were not legitimately married - or if they are, they are beyond ignorant on the matter.
They are saying your marriage is not sacramental. Major difference.
And as noted in the thread above, your baptism makes the marriage sacramental.
I understand your anger, but you are getting matters mixed up between a sacramental marriage, and a legal marriage.
Your RCIA coordinator is trying to explain that your marriage is now a sacrament - and may not be doing it very well, or may be running into your anger - and the anger is very understandable.
As your wife is joining the Church also, if I understand correctly, what does she want to do? And I am asking, not if she is willing to go along with whatever you decide - but what does she actually want to do? She, too, is part of this process.