If I understand the original post correctly, el dominicano has lived in his new home country for the past 20 years, and he has lived with Number 2 for 12+ years there. He has only spent 15 days a year for the past 12 years with Number 1 here in the DR.
Most other countries laws would now consider him to be the common-law wife of Number 2, and I think the DR legal system would consider him to NOT be the common law husband of Number 1, because he is not here in her house or in the DR for enough time to be legally found as such.
ALL of the kids should be considered his heirs if he dies, but again, getting a claim on whatever he leaves behind in another country (and this works in BOTH countries where he has children) would be extremely hard to do. Even with a recognized claim, collecting is another thing. By the time the justice system of most countries worked, Number 2 would have managed to put them out of reach by any means, for both her and their childrens' future security.
If I were Number 2, and we had managed to build up something substantial together, I would be pressing him to finally get legally married, but that depends on the laws of the country they live in. If she failed to get him in front of a judge to be legally married, and for the security of knowing she would get 1/2 for her future, she would at least have a choice to make a claim to her share of the assets.
Number 1 should probably be thankful she gets to see him at all, and for anything he gives her. I am positive he comes home with armfuls of things for his kids here when he comes, that is the dominican way. Maybe he stays with Number 1 to see his kids here in the DR and to avoid having to pay for a hotel during his "vacation" in the DR, who knows?