Problem with Staff Grouping

[Dave Higgins]

I'm transcribing a piece that has multiple parts and in those multiple
parts, I have multiple staves.

After compiling, the staff layout becomes:
part1:staff1
part2:staff1
part1:staff2
part2:staff2

Obviously for the score, I'd like:
part1:staff1
part1:staff2
part2:staff1
part2:staff2

I'm sure I just have something not correct.

violinOne = \relative c' {
    << { b2 b } \new Staff { g g } >> }
---
violinTwo = \relative c' {
    << { e2 e } \new Staff { e e } >> }
---
\include "violin1.ly"
\include "violin2.ly"
\score
{ << \new StaffGroup = "StaffGroup_strings"
<< \new GrandStaff = "violins"
<<
\new Staff = "violini" { \set Staff.instrumentName = "Violin I."
\violinOne }
\new Staff = "violinii" { \set Staff.instrumentName = "Violin II."
\violinTwo } >> >> >> }
---
\include "violin1.ly"
\score
{
<< \new GrandStaff = "violins"
<< \new Staff = "violini" { \set Staff.instrumentName = "Violin I."
\violinOne }
>> >>
}
---
\include "violin2.ly"
\score
{
<< \new GrandStaff = "violins"
<< \new Staff = "violinii" { \set Staff.instrumentName = "Violin II."
\violinTwo } >> >>
}