She has a hard time recognizing that the feelings are coming from her
This is really a great point.
Instead of looking inwards for why she feels insecure, she looks outwards to find a reason. Instead of owning that she has poor self-esteem and needs validation supplied from others, she looks for excuses for being upset, feeling like you're going to leave her, and then goes off on those things as if they are facts.
Sadly, to "fix" things with your mom you may need to give your om a crash course in BPD validation. Your mom would need to work on being an ally to your GF, not an enemy, without triangulating against you.
Jealousy - very common. They FEEL you plan to leave them. So obviously you must be cheating for them to feel this way. Even if you work to be 100% open, that fear is in there. H is the one who was likely to cheat, but he always accuses me of it when he hits certain moods. I find the best I can do in these cases is show, not tell, that I care and am not a cheat. hard to explain, not easy to do, but it's all I can really suggest.