That tool you emailed me seems to only keep track of NameServers, which is not the same as your DNS registrar. When I checked on my own domain, it tells me who owns my nameservers (i.e. DreamHost), but not where the Domain is registered (i.e. NameCheap, just as an example). Yours says you did transfer the nameservers to DreamHost, but that doesn't guarantee that the registrar change was complete. When I look at the account's panel for DNS, it even says 'To modify your domain's whois information, please visit the registrar you registered domain.com with (looks like it's not us!)' so somehow that just didn't get finished.
Since the domain registration isn't supposed to be able to magically switch back without intervention, the most likely scenario is that you changed the nameservers and the DNS registration never finished the transfer, so when it expired on 1&1, you ended up in this mess
Once you get control back, you can complete the registrar transfer and verify in the panel that it's changed (it'll say that your registrar is us) or a WHOIS check which will have us listed under "Registrar". If that's not changing, then that's where the problem is
I'm really sorry this is such a hassle. DNS registration is still the worst part of websites, IMO. Most people never move them because it's such a hassle (when I started with this, I had to fax people).