1) Depends somewhat on how everything in that 3-way circuit is wired , from the supply line out. If you can post a diagram or describe it in detail, that would help.
2) A splice is allowed, but it has to be done in a junction box and that box has to be accessible. Note that this doesn't mean you have to splice at the end of the existing cable -- if you can more easily provide an accessible box somewhere earlier in the cable run, that's OK.
Note: I'm an amateur; a real electrician might have other (and better) advice. Note also that this advice assumes you're in the US, which may be wrong.