Is she as fixated on you, as you are on her? Really? She already has 4 kids in her life, so it's easy to understand that the LAST thing she wants or needs is another one. Also, as been pointed out, you've only known her 6 months and all you can talk about is kids, kids, kids....no mention of marriage. Perhaps you see a child as a way of "marking your territory".

Look....this lady is smart enough not to have children with you. You want kids, you need a plan "B". What is it?