Whether you want what you said or what you described, preamp first, then split and crossover. Otherwise the crossover is playing with your wimpy out of the bass signal, not a nice preamped signal, and will also affect the bass/clean signal.
What you described was full signal to bassamp, and highs to guitar amp, which would be split to bass and high-pass, and high-pass out to guitar amp.
What you diagrammed was split to crossover (both high and low pass) with lows to bass amp and highs to guitar amp - which is fairly normal, but not what you described with "full" or "most frequencies" going to the bass amp.
Best device - depends what you have, or if you have a budget. My $80 TNT 130's preamp could do either of the things you asked, depending what you plugged into what. Assuming your bass amp has a pre out and a power in, but no crossover section, come out of the pre out with a split cable, run one into the power amp in if you want "full signal" to the bass amp. The other goes to a high pass (or crossover with only the high out connected) an on to the guitar amp. Otherwise, come out with a single cable, into a crossover, and run the low cable back in to the power in, and the high to the guitar amp, if that's what you want.
In either case, put a preamp in place before you split the signal (unless you have a preamp in the bass, ie, an active bass, in which case, you have already got that part covered.)
I've seen TNTs as low as $65, sometimes they go for free - you could pull the electronics head, toss the mondo transformer, and put it in a small case with a lightweight power supply for the preamp section only (+/- 15V) and trim it down to a manageable weight & size - but you can probably also get a pedal or the like that will do the same for you in an even smaller package. I just happen to know that this has everything needed to manage either thing you've asked for in a convenient package (wrapped in an inconvenient package with a speaker in it.)
Here's an elderly thread about more convenient options. Crossover pedal????
At the end of which is this option that will also do all you ask, either way, and is evidently made by a TB-er.