Toddler discipline - help!

[Smoke Jaguar]

I agree with Bec - I think there's a bit of memory-enhancement going on with your mum, Nee...my mum does it all the time. Every time DS falls over and hurts himself she tells me she never let me fall over so that I never had to cry...yeah, right!!
Regardless, you need to tell her that as it obviously isn't working for your DD, she can either allow you to babyproof the house, or she can tell the coroner how she insisted that just telling her own daughter 'no' as a child was sufficient and she thought her memory was enough of a safety measure.
My dad refused to move certain things in his house and would have conniptions saying 'dont' let him do that, he'll brain himself'...and totally disregard me when I'd ask to him just put it somewhere DS couldn't access. I have no idea why some people are so against changing their physical environment (let alone their mentality) for children, as if they're selling their souls or something hideous, instead of protecting little ones I mean, if it's really that important to these people, they can just move everything back later on...it's not for that long, anyway.
If she insists that she cannot move anything out of harm's way for the sake of her granddaughter, then I, too, suggest finding your own place in the interim. It's not worth it, should anything happen - you need to stand up for your DD's safety, rather than living to regret that you didn't. It's like any occupational health and safety guide will tell you - the first and best measure is to remove the hazard, next if you can't do the first is to make the hazard safe (fire grate, like Bec suggested...boxes were never going to work!). We have these things enshrined in Codes of Practice for adults, and think that children should just 'know' better in an adult environment??
I'll just reiterate: once something has been identified as a hazard, it is negligent (and then punishable by law in a workplace environment at the very least) to do nothing about it. And god absolutely forbid the hazard becomes the cause of grievous injury for having been left there.
And I never believed that my mum never let me fall over when I became mobile. And she knows I don't!

ETA:
Emma, you may be onto something. My niece has been into books, reading and talking for a very long time. She is also capable of understanding when something is not to be touched or climbed etc. She was never as physical as my DS, though she may become so later on.
My DS has always been physically oriented (crawling at 4 and a half months, no mercy for me!), and a very 'trial and error' child. I took him to a term of music for kids and every week had a barnacle on my arm who would not engage and kept running to the window to point at the playground. He is only now starting to be interested in books...but not so much for reading as the pictures that go in them. He is getting into music slowly now, as our Kindergym program incorporates it in the classes. He likes to be thrown around on the floor and in the air, loves to sit and trot on my horse, chase dogs, run and tumble. He is very much a 'head first' kid. No amount of talking or saying 'no' was every going to deter him from touching and moving things.
I absolutely reject that this is because of 'bad training'. These are the reasons why: I have an English major and had a great line-up of books to read to my child before he was born and have always loved reading (duh! would want to in order to do 3 years of literature at uni!). I read poetry to him as a small baby to help him get to sleep but after about 5 weeks he just wanted to be walked around in the sling instead (books have been for throwing until recently). As for music, I'm a singer and we have a house full of instruments...no go there, either - only 'Wiggly Safari' has brought him closer to music appreciation...so I have Steve Irwin to thank!
Therefore, I really disagree that all kids can just be coached to listen to you from a young age (though, as Charlyfrog suggest, you CAN start using the words with her, even if she can't consolidate the words with what you want or don't want from her right now). There are cautious kids who 'listen' or 'think' their way around their environment and there are 'trial and error' kids who 'feel' their world (which ties into the Neuro Linguistic Programming idea that everyone has a communication style that is predominantly listening, feeling, or information processing) in the first few years. This will be the pattern until they are a bit older and all processes developmentally start to catch up (like DS starting to listen to me instead of me having to show him, and starting to use a lot more words now...though more degree of difficulty in his case because he's growing up bilingual).
Anyway, this is a theoretical approach to they why's and wherefore's.
Meanwhile, it's bloody-mindedness to me to leave a house un-baby-proofed for a physically-oriented kid when you are aware of what the hazards are.