Hmmmm... After chasing the woman away, and should the contract lady succumb to your request and you later got married later. Then she becomes a step mom to "your" child. What if she's cruel or behaves the same way majority of step mommas behaves??
The child may grow up out of depression, hatred and other social vices.
Its better you sit your fiance down, and talk to her as if you're brothers and sisters. If you chase her out, and she did her research, and she find out you later married the contract lady. There's 90% probability that she's likely to harm both of you.
I won't advise you to chase her out, as others said.
Just sit her down and explain everything to her.
Remember to go for a DNA test to be sure you're the biological father of the girl.