It is hard for me to understand your situation. My response was within my own concept and understanding of relationships and marriage. When a third party is introduced by way of an affair, or by consent as it is in polygamist type arrangements, that is one thing. But, where children are produced as a result of this type of arrangement, I can't help but think, what is in the best interest of these children.
When you said:
But my only desire in life is to be someone's wife and be the only one... I don't want to be second best.
... I believed this to be brutally honest. Wanting to be someone's wife, and the only one, and not be second best, is not wishful thinking as you now imply. Nor is it in my opinion, a fantasy, or unrealistic.
It is not up to anyone to judge your living arrangements, but you. Unless of course this man is also 'married' to several women at the same time and has produced more children than he already has. In which case, we have laws to protect children living under these circumstances.
So how you decide to live is only your decision. You do have the freedom to choose a different life for yourself and your children. I think the old flame coming into the picture has opened up at least thinking about that possibility. But should you choose to remain where you are, then that choice is yours to make.
That you are entertaining the idea of defining what you want, as in your statement above, you may falter back and forth about it for some time. But, it may eventually lead you to take action to change, and if that ever happens, I do hope that you come back again. There are many here who can offer good advice on how to make changes possible.
Best of luck to you.