the US bishops have addressed this concern by dedicating this current catechetical year to Matrimony-sacrament of enduring love and urging pastors and catechetical leaders to emphasize teaching on the sacramental nature of marriage in the context of the Church and unity with Christ, and making efforts to invite those with any irregular situation to be welcomed and assisted to regularize that circumstance.
They couple begins by setting up an inteview with the priest or deacon to lay out all the facts of their situation, they receive pastoral care including sacramental confession as appropriate, are assisted with investigating any past marriages to determine validity and their own current options, and when possible, in convalidating the present union in the Church. That includes pastoral care, counselling, marriage preparation and all other assistance available to couples and families, suited to the needs of that particular couple.
The individual Catholic involved in a union with a person who is not interested in complying with Catholic thouht on marriage is assisted pastorally, as an individual, to find solutions to their moral dilemma, while regarding practical matters such as finances and most especially, care for any children involved.
There is always a remedy for any situation.
Rarely does finding that remedy follow a time plan dictated by either party to the relationship or by pastors, but is guided, when he is invited to be present, by the Holy Spirit.
this completely misstates Catholic teaching on the status of children of unmarried persons or those in irregular unions.
If you want individual answers to the individuals disparate issues you raise, search for past threads on those topics: divorce, annulment etc (none of which effects the status of children). Where did you get the idea that the church does not “recognize” children of those whose parents are not validly married?
You or I as a parishioner in the pew cannot judge the state of the soul of anyone receiving communion. That perogative belongs to God alone, and as excercised by the priest in the private forum (confession). You do not and cannot know all the facts of the situation. If it were easy to look at any relationship or family from the outside and know all the facts, there would be no need for a formal investigation of their status. Annulment proceedings are private and remain so for good reason.
If someone approaches you personally with a question of information, refer them to their pastor.