The big problem you're going to have with all of that is ground loop noise with the PC. It is very common to find that trying to connect the USB audio interface to a bunch of guitar pedals and amps and such causes ground loop currents that equate to hum in the signal.
However, this should be 100% fixed by just making the right cables. If you have a vaguely new USB audio interface, you just need to make a cable that takes a low impedance output from some pedal that's known to have a good low impedance out, and adapts that to the balanced XLR input (or balanced TRS if the interface has one). See this page:
https://www.ranecommercial.com/kb_article.php?article=2107
You want connection diagram 13 (or 14).
Note: The guitar needs a really solid earth connection. This should be provided either by the guitar amp.
For capture, you need a pedal like the livewire thing I have that has a "through" connection or equivalent pedal that splits the unmodified signal to the amp and then outputs to said cable to your USB interface.
Note: The livewire ADI direct box (LWADI) would work stock EXCEPT for the fact that the input impedance is only ~175K. So you could use it with a clean buffer in front. Or you can change the two resistors as described in my mods and get the impedance higer. But even then, it will be in parallel with your amp which is probably 1M so the impedance seen by the guitar would only be around 400K which is probably ok but some real pedants might take exception to it. So you might just use a clean buffer in front of the LWADI.
For re-amp, you can make another cable but this depends on whether or not the USB audio interface has a balanced output or not. If it does, then use connection diagram 5 probably and just plug right into the amp or pedal board or clean buffer. If it's not balanced, you probably want connection diagram 3 but in this case you are connecting grounds so you might get hum. This is another place where the simple impedance balanced single op amp device I originally mentioned would be good.
Re-amping will definitely require a bit of experimentation. I would just get your cables right as described above and verify that you can capture and re-amp without hum from ground connections. Leave out the pedal board. Play with the levels. If you re-amp into the LWADI you can simultaneously record loopback and verify that the levels are correct. You can also invert and mix the capture track with the re-amp capture and verify that they sum to zero and that they are therefore identical in signal and level.
This is all just thinking out loud though. If I were doing this, I'm sure I would find little issues that need to be tweaked to get a re-amping rig correct.
Note that a lot of comments on the Internet about reamping and devices that are advertised as being good for reamping are total BS. If you invert and mix as described previously and the two signals are verified to be identical, then your good.