Sometimes it is easier to copy source to target for a given segment, but then searching a word from target searches target in TM as well. So rarely do I actually want to search the target that I think a toggle/option for this would be better (cf. memoQ).
Or, simply doing step 3 when necessary would do.
Sorry if I'm mistaken.
OK, If I understand correctly, while ALT+ENTER cannot be used from target segment, you can still :
Select the word or text you want to check (in either source or target segment).
Press Ctrl+Shift+F4 to launch a source TM search, and Ctlr+Shift+F5 to launch a target TM search.
Ctlr+Shift+F9 is for MT search, but it won't work for target, since the language pair direction is already set.
You can also use the Quick Search Bar. If it is not displayed, go to Edit>Quick Search or press Ctrl+Shift+F.
Then, just press the button TM source or TM target to search.
Lastly, it's easy to go from target to source segment with the keyboard: Use F12 or set Tab key to cycle focus : View>Segment editors>Cycle focus with Tab key.
PS, to Igor: I think the Quick Search Bar is hidden by default. Which is a pity, since it's an extremely useful CT feature for launching all kinds of concordance and other searches, along with Ctlr+F. New users do not know the keyboard shortcuts yet, so it would make sense to leave it on by default.