Hi, like you I have two Toodledo accounts. I found the best way to see both lists is to get another app on the iPad and use the Toodledo app for one list and the other app for the other list. I picked an app called 2Do but there are others that also work with the Toodledo database.
I wouldn't use this tool to schedule a meeting. I tend to use this tool to remind me to book a meeting, I also have a context called "Meeting" where I jot down items that need to be discussed at my staff meeting.
I had that same issue so, whilst it cost more, I actually got a second pro subscription of TD. I then use the sharing functionality and can easily skip between my work and home lists. The issue is then on portable devices, so for these I use the TD iPhone/iPad app and the 2Do app pointing to the different lists. It works and allows me to have slight different set-up for work and home.