Hi MookiesMatter, and welcome to WebmasterWorld.
Several comments... Google Trends is useful only for searches with lots of volume. It is not what I'd call a very "granular" tool otherwise. So it's extremely unlikely that Trends would show searches for your particular domain, and even less likely for a more specific search combining your domain name and an adjective.
Suggest was a Labs project before it became a standard feature on the search box. In the Labs incarnation and in the early days of the search box implementation, numbers were returned along with the phrases. The numbers then reflected the number of pages returned, not search popularity.
Ultimately, Google dropped the numbers, and I think the official word (or popular supposition) was that they did so because they were distracting and people weren't really looking at them. But it's also likely that Google dropped these because they had factored other considerations into the personalized (and perhaps other) configurations of the tool, that the numbers therefore weren't really correlating any more with what the tool was showing in the personalized setup, and it was too complicated to switch displays.
Google's Web Search Help says that historical data is used only when you're logged in, so it may be that you're seeing what you're seeing because you are logged in. In the More about Google Suggest [google.com] section of the Help page, Google describes it this way...
I don't know if you're seeing the problematic suggestions just when you're signed in, or all the time.
Also, if you are signed in... it's not clear from the Google Help description how much your own historical searches are affecting the results you're seeing, vs historical searches from everyone else.
It may be that you're skewing the results just for yourself, or that if you're searching too much for "MyDomain.com sucks", skewing the results for everyone. You'd have to sign out, flush cookies, and sign in under a different account to observe differences.
As an aside to this, there is currently in the Supporters Forum a discussion about what features a useful autosuggest tool should have....
WebmasterWorld Supporters only...
The Importance Of Autosuggest For Search & Ecommerce