WinHTTP and embedded IE working on one the same session

Hello.
I've got a problem, I'm writing a program, which allowes you to use website normally on embedded IE and WinHTTP will working in the background to automate some activities.
There's my question, because this site is using SSL token in the cookies to handle session, so log in via IE is killing WinHTTP session and vice versa.
is there any solution to make them use the same cookies? Or maybe any other way to share / import cookies?
Or maybe any proxy will resolve this problem?
Could you please help me with this problem?
It's core of my program, so without it, it's useless.
Greeting, genotypek.

Hello.
I've got a problem, I'm writing a program, which allowes an user to use website normally on embedded IE (It's irrelevant in this situation, IE can be even oppened standardly from it's exe) and WinHTTP/WinINet will working in the background to automate some activities.
There's my question, because this site is using SSL token in the cookies to handle session, so log in via IE is killing WinHTTP session and vice versa.
is there any solution to make them use the same cookies / handle same session at one time? Or maybe any other way to share / import cookies?
Or maybe any proxy will resolve this problem?
Could you please help me with this problem?
It's core of my program, so without it, it's useless.
Greeting, genotypek.

[Thread moved in response to OP]