Do you have 12 months in a row of proof of living together in the same room? With that, and the other proof, you would most likely be successful. Without it, it really depends on the visa officer as to whether he or she will be willing to 'read between the lines' and assume you were together for some periods where you lack proof.
It sounds like you have proof for 3 months, 5 months, 1 month with one mother, 1 month with the other, and 1 month in hostels/hotels.
The bank statements are great, and may make up for any missing proof of cohabitation.
You could apply with what you have. If accepted, great. Meanwhile, continue gathering proof of cohabitation and the genuineness of your relationship. Then if refused, don't appeal - just use your new evidence to reapply.