whats the scale length? the shorter it is the more tension on the string to get to pitch.. maybe try the B string instead of the G and see if that tunes up to pitch?
If your using the A, D and G strings from a regular pack of guitar strings and tuning those strings to G-D-g, the lowest string (the A string from a regular pack of strings) should be tuned one whole step (two semitones) lower than A (on a regular guitar) - which would be G.
The other two strings (D and G) are tuned to the exact same pitch as they are on a regular six string guitar so, you should not be breaking strings at all unless you are trying to tune an octave higher than what you should be tuning.
If you are using a guitar tuner, make sure to set it to "chromatic" scaling instead of "guitar", "ukulele" or "violin" scaling. This could be causing the problem.
BTW - String tension decreases as the scale length decreases. In other words, the longer the scale length, the greater the tension needed to bring a string to the same relative pitch.
You are obviously trying to tune the low G an octave above what it should be. Also with that other tuning, taking that "D" string to to a B, you are trying to take it 9 semitones higher than it is intended, that's why it's breaking. If you are tuning with digital tuner, it's not great for beginners- it's better to use a tuning fork, pitch pipe, piano or harmonica to strike a note then you can actually HEAR what the note should be.
For EBe tunings, I use the EAD strings from a 6 string pack, .042/.032/.024. on a 25" scale. This gives a lower tone, which is how I like 'em. These three strings also work for me on GDg, also presenting a lower, bassier tone.
In Guitar mode the tuner only knows the notes E2 A2 D3 G3 B3 E4 and won't show the other notes.
you're after G2 D3 G3, and the tuner only knows G3, one octave higher than G2 - and KAPOW
Same with the E2 B2 E3 tuning you want, D string dropped to B2, but in guitar mode it only knows B3, an octave higher. You're probably also either getting a very floppy G string down tuned to E2, or breaking it trying to get up to E4
An easy rule of thumb - from a floppy string that makes no sound, tighten just enough to get some tension where it will sustain a pluck, then tune up to the FIRST occurrence of the note you are after (using a chromatic tuner). Guitar strings have a tad more than a half-octave range either side of their design spec and still work well enough.
I love a nice low EBE tuning for rockabilly, country and Mississippi hill country blues.
I use Chickenbone John's Med balanced tension G-D-G strings (46w, 30w, 22w) tuned down - sounds a treat and you can bend notes to buggery. Sounds great with slapback and reverb.