1. my girlfriend lives in PA, i live in NJ right across the river. In PA, tasers are illegal in philadelphia. They are illegal in NJ everywhere.
Tasers are illegal in Philly? No kidding? That I have to look up. My PA CCW is valid everywhere in PA including Philly. So I'll skip carrying a taser, and just carry a pistol.
If your girlfriend is 21, you might want to ask her to apply for a PA CCW. Cheap, usually around $20, with no training requirements. I gather she currently does not own any firearms, but with a CCW she can very quickly change that situation.
2. it is not a stun gun. it does not shoot out wires with electrodes. it is a contact electrical incapcitiation device. 300,000 volts.
Tasers are the electrical incapcitiation devices that shoot out wires with electrodes. Stun guns have two poles, between which an arc of electricity passes. Stun guns are the "contact" device. (Direct contact isn't actually needed. Close counts. Work as an electrician for a while and you will learn this.)
3. I am on great terms with her mom. any argument I will have will be on good terms and no harm can come from it. her house her rules no matter how nuts.
4. my girlfriend does carry mace (CS military tear gas w/ 10% pepper spray)
thats the thing she can get to fast if shes in trouble.
Careful mano. I've been on good terms with some of my ex's mothers, but tread carefully. Women have an infinitely higher potential for viciousness. All and all, as long as your girlfriend lives under her mom's roof... Mom's rules. You know this already. Might be a slight motivation for your girlfriend to move off on her own.
Out of curiousity, has your girlfriend actually practiced with said mace? If not, I'd recommend doing so. I know a few people that temperarily blinded themselves before they didn't consider wind can carry some of the spray... You and your girlfriend could take various self-defense courses together.