De they mean the same thing? and sound natural?
1) l don't mind traveling all the way there, even if I could only see her once.
2) l don't mind traveling all the way there, even if only to see her once.

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Answer

Both are perfect.

In #1, I would prefer "can" to "could" since "I don't mind" is not conditional.

I like #2 with no changes.

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Natural are:

I don’t mind traveling all the way there, even if I can only see her one time.

I don’t mind traveling all the way there, even if I only get to see her once.

I don’t mind traveling all the way there - even to see her just once.

If I could see her even once, I wouldn’t mind traveling all the way there.

Your ‘could’ sounds wrong (though the type of error made by native speakers) unless it is part of a conditional such as in my last example.

Answer

2)".... even if i only see her once". you need to delete the "to".

1) I am not a fan of this sentence. the word "could" doesn't do anything useful for me.