Thank you for your responses. I think my question was not precise enough.
I solved my problem using an iframe with the first login page as the source.
<iframe id = "iframe1" name ="loginFrame" src="http://domain2/Login.aspx?for_web=true" onload="iframeLoaded" ></iframe>
To redirect to the default start page on the first site, added OnClientClick = "formWeb.target = '_ parent';" on the login button. Therefore, when the "Login" button is pressed, in case of successful authentication, the default page (in another domain) will be opened in the same window (and not in the frame).
<form id="formWeb" runat="server"> <asp:Button ID="btnLogin" runat="server" Text="Login" OnClick="btnLogin_Click" OnClientClick="formWeb.target ='_parent';" /> </form>
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