WHOA WHOA WHOA just wait a minute there before you start writing off child protective services as a non-issue.
If you read stories on reddit, national newspapers, or even the local news, you will see that the police and CPS can be EXTREMELY dangerous to deal with. If you allow your children to go to a park, you may have your children taken away. If your child is outside in the front yard behind a locked gate, they may fine you for leaving children unsupervised.
That is if they don't call the police to point guns at you, your children, and you family dog.
Your mother has no idea how dangerous what she threatened really is. Would she feel the same sense of entitlement when she sees her daughter gunned down by the police on the news? Too bad it is too fucking late by that point and the wrong people are punished.
"If you're carrying anything else, we'll open fire." - The police to a father who was asked for ID IN FRONT OF HIS SMALL CHILDREN UNDER 10!!!!
1) Keep records of EVERYTHING she sends you.
Record the voicemails, save the text messages, record the phone calls, and keep it somewhere safe where it can be referenced.
2) Take photographs of your home at various times in various states of mess. YOU DO NOT WANT THIS TO BE CLEAN AND IMMACULATE IN EVERY PHOTO!!! THAT IS EXTREMELY IMPORTANT!!!!
It may also be a good idea to include photos of happy children without bruises, marks, and so on.
If they claim the home is unsafe, you can respond with your own evidence.
3) Understand that she is a threat. An actual, literal, real life threat like a bear, cougar, or other violent creature.
If she calls child protective services and lies through her teeth, there is no way to know what will happen. You may end up with a raid on your home, dog gunned down for "attacking police", and whatever charges they can dream up as they haul your children away. It will be massively expensive to get them back and clear up the charges not even considering the virtual nuclear bomb it drops in your personal lives.
Your children are in real danger and she is the reason.
4) After you have collected the evidence you need, seal it in a glued envelope, take it to USPS, and have them put it in a priority mail envelope sealed with their materials then mail it to yourself. This, known as poor man's copyright, can go a long way to making the various bits of media admissible in Court with specific dates/times attached.
No one should have to go through this, but takes CPS threats extremely seriously. They are no joke in 2014. Far too many people have to sign documents giving CPS rights to home inspections and various other things just to keep their children from being taken.
That isn't even considering the cases where parents have had their children taken away for just 2 - 4 weeks to find they were victims of rape and sexual violence during those times..
TL;DR Please take this seriously. The last thing anyone wants is a follow up/update on it getting much worse.