When you use ASP.NET Forms Authentication a ASPXAUTH cookie is created for that domain.
Cookies are sent with each request so ASP.NET will look for the ASPXAUTH cookie (which doesn't exist in domain2.com) and determine that the user is not authenticated.
You might have to look into a cross domain SSO solution that fits your needs. Have a look here: http://www.codeproject.com/Articles/106439/Single-Sign-On-SSO-for-cross-domain-ASP-NET-applic