Nothing wrong with chalk - it washes away easily enough. And there is no law against touching walls either.
Just because someone is old, it doesn't mean you have to treat them with kid gloves. A nasty old person, is just a nasty young person, a few years down the line. In fact, I actually know of an old woman who had an asbo - I think she used to throw rocks at her neighbours children. She made their lives a misery.
I think you have to stand up for yourself. Tell her if you see her going through your rubbish again, you will call the police. If your flats are rented, can you contact the land lord or housing association?
I find it very offensive for adults tell children off, when their parents are right there. It's treating you very disrespectfully and you really shouldn't put up with it. There is nothing wrong in telling her to address her remarks to you and not your children.
I think you have to do something, or she will continue to badger you. and your dc need to see their mother stick up for them, because if you don't do it, who will?