OP ill only say this one more time your best bet is a hall pass or 3some (though u said that isnt an option, perhaps the MMF idea will help haha)

seriously though if you truly care about your gf this will fuck up your relationship. it sounds like ur thinking with ur dick and not thinking of all the consequences with her and her brother etc. it could end up ruining your life. and then that other girl will probably suck in the sack. or her period will start and ruin it.

im just saying the universe works in pretty obvious ways and this shit never works out for anyone

so you should just be honest with ur gf and get some permission. or be honest about how u feel and maybe the sex life will reignite