If she is this jealous and controlling after 2 dates, then you can expect it to only get worse....Some examples for you to look forward to:
Expect to have to "check in" at least twice daily and tell her where you are and what you are doing. expect to have many arguments about your roving eyes while out in public. Expect her to censor your TV / magazine / internet viewing as she can't tolerate your looking at other women.
I was seriously involved with a woman whose terrible jealousy came to the surface after a couple of months, it became obvious to me this was where i was headed so i terminated the relationship.