I used to take a 1 x 15" peavey bass combo, and a 2 x 12" guitar combo to all my gigs, and some of these were smaller pubs. I never had a problem or anyone laughing. I would often be complimented on the sound in fact!
EDIT: Back on topic, the DI output from your head will be at line-level, so it'd be best to put it into the return of the 2nd amp. However, if you wanted to use separate EQ on the 2nd amp, and you didn't want to take a splitter of some kind (most tuners have 2 outputs) then you could get away going from the DI on the 1st amp into the input on the 2nd. You'd just have to have the input gain pretty low