I think the structure is clear?
"there are...":the main clause
"to which...":the attributive clause of "no lengths".
no lengths to which she would not go
= she would not go to no lengths
= she would go to a lot of lengths
= she would try hard or try every effort (to do anything)
the "none" means definitely "no lengths"
= there are no lengths,none,definitely no lengths
= definitely try every effort
"rather than...":the main clause in respect to "there are.." to express perference.
= she would try every effort (to make sure) that I did anything (or I could do anything else) rather than I marry another woman.
The whole sentence is something like:
There are definitely no lengths to which she would not go (to make sure I should do anything else) rather than I should marry another woman.