Share a cookie between two websites
Cookies are only accessible to a single domain that they are set to.
I believe if you are using two sub-domains on the same domain it would be possible to share the cookies, however the browser doesn't send cookies set on one domain to any others.
Edit: You also want to avoid storing large amounts of data in a cookie. Is there perhaps the chance you could create an api that site B could query with javascript?
No. Website B can't read a cookie from website A.
The easiest work-around is to pass login/credential information from website A to website B and have website B set a seperate cookie. For example, after logging into website A you could have them quickly redirected to website B with an encrypted querystring. Website B could then read the information, set its own cookie, and redirect the user back to site A.
It's messy but possible.
You mentioned the same company owns both sites. As you suspected, if the sites have the same domain like www.mycompany.com and store.mycompany.com, then they can share cookies. The HTTP response header would look something like this:
Set-Cookie: user_id=1295214458; Path=/; Domain=.mycompany.com
Since the client has direct access to this data, you should also include a signature so tampering would be detected. Usually the whole thing is encrypted and signed into a "token", and that is set as the cookie. But technically, just the signature is required.
If in your case all your users use browsers with HTML5 support you can use window.postMessage method that allows to addEventListener on one side and to postMessage from the other. Here is a nice article/example: https://developer.mozilla.org/en-US/docs/Web/API/window.postMessage.
Then the steps are simple:
- add to site A a hidden iframe to site B
- send B's cookie to A using window.postMessage
- store the received cookie in A's cookie