I can understand it. She's addicted to babies. At least she started saying she wanted 'just one more' at a year-I said let's do it again when my twins were 3 weeks old.
If you really don't want any more (and I certainly can see your point-4 is a lot-I'm the oldest of 4), make that really clear. Then get a vasectomy. It's possible she's lamenting the end of infancy in the youngest. I know my mother was very sad when my brother wasn't a baby any more, knowing he was the last one. She had foster parent papers filled out, thought about adoption...the fear of not having a baby in the house was that strong for her. And I think on some level, churning out babies might make her feel like she's not getting older and that she's still productive.
There's physical downsides to constantly having babies as well so although the whole process is an enjoyable thing, it really ruins a woman's body in the long run. And at some point, she WILL have to stop. Take it from someone who had kids late in life-stopping early will only benefit both of you down the line, in married life together, physically for her and even for the kids you now have.