Irule to redirect all traffic to one domain to another.

It will generally depend on where everything lives. The easiest thing would be if website.mydomain1.com and website.mydomain2.com were on separate VIPs with separate IPs. In that case, any request to website.mydomain1.com could simply be HTTP redirected to website.mydomain2.com (to the other VIP). You'd want to keep the separate 80 and 443 VIPs though, as you'd need to know whether or not to decrypt before injecting an HTTP redirect (you can insert a redirect in an encrypted packet).

If the two URLs live on the same VIP (same IP), then it gets a little trickier. You still need to keep the website.mydomain1.com SSL certificates alive so that you can decrypt and inject a redirect without the user getting a certificate error. To do this you'd attach both client SSL profiles to the VIP and assign each a corresponding Server Name value that corresponds to website.mydomain1.com or website.mydomain2.com. The VIP will select the correct profile and server cert based on the SNI in the client's request. Then you can use an iRule that looks at the HTTP::host value, and if website.mydomain1.com, issue a redirect to website.mydomain2.com. Also keep a running log of when users access the site via website.mydomain1.com so you know when it's safe to remove the old client SSL profile and redirect iRule.

when HTTP_REQUEST { Redirect from / to actal URL. HTTP::redirect https://website.domain1.com }