Hi Samuel,
I understand why it makes sense from a user experience perspective, although I'd be a little concerned that it would be a bit weird, especially if the domains are branded differently.
I'd probably start by avoiding an automatic redirect. The simplest option is probably to include a prominent CTA on the desktop version that says 'view mobile version at www.otherdomain.com'. If you want to get a bit fancier, you could display a message when a mobile user agent is detected, saying something like 'it looks like you're on a mobile device. Would you like to view a mobile-friendly version of this page?'. If you do this, make sure that
- a) the page is still accessible to a crawler with a mobile user agent (in other words, don't require input from the mobile user in order to view the desktop version, just include it as an option)
- b) use a cookie to avoid asking your mobile users to answer the question again every time they visit.
If you really want to do the redirect, start by testing on just a couple pages to check for any negative impact before rolling it out further.