Why does it bother your girlfriend for your mother to go to church with you? Why is church your alone time? Do you and your girlfriend usually get coffee, tea, lunch, etc. after church or something?
Do you have a small group or life group that you get together with regularly/semi-regularly for bible study and discipleship?
Honestly, unless your mother is with you in all your time together, I'm rather puzzled as to why your girlfriend is upset about your mother attending church with you guys since church is about worship, fellowship with other believers, and guiding and strengthening your relationship with God.
You said for a month you had one Sunday where you'd go to church alone together and the other Sundays/weekends you had other activities planned for the two of you to have time together without Mom. If you were doing this then I'm again rather stumped as to what is actually upsetting your girlfriend here since that would be the alone time she wanted.
Is your Mom pushy? Did something happen that created bad feelings between your mother and your girlfriend? Has your girlfriend thought of building a relationship with your mother apart from your relationship? Like having a ladies day or something every once in a while?
Have you considered and/or tried asking your pastor or a church elder for advice? Someone local who knows all three of you may have more insight on how best to proceed.