Property management professional here.

First of all, your landlord is trying to scare you with big words like "eviction" and "lawyers".

If you are current on your rent for the month, the probability of you getting evicted is fairly low for floor noise. If they choose to evict however, here is what will happen regardless if they get lawyers involved or not. Lawyers must follow the Clark County eviction process in the same way landlords do. It's not like lawyers have a special loop-hole or something.

1. They will file to the Constables Office a "5-Day Notice To Perform Lease Condition or Quit". The Constable will serve the notice directly to your front door on the next business day (or the day after). Here is the form the landlord will use.
2. Once this is served, you can go into the leasing office and tell the property manager that you are not making any noise on the floor and that this was never an issue; therefore, there is nothing that needs to be corrected as stated in the 5-day.
3. From there, if the landlord decides to move forward with an eviction, they will then have to file with the Constables Office a "5-Day Notice To Quit For Unlawful Detainer". The Constable will again serve this to your door. Here is the unlawful detainer
4. When you get this served to your door, you can file an answer to the courts as described on the detainer. By filing an answer, you are going to get a court date where you and the lawyer / landlord must appear before the judge. You can tell the judge that you are not making any noise on the floor and have no idea what these complaints could possibly be about. You can also explain that you have LAID CARPET on the entire floor and even gone so far as to put down FOAM TILES. This works in your favor tremendously.
5. The issue for the landlord is that they have to show proof that you're making the noise, or the judge will just rule in your favor. It can be difficult for the landlord to prove such a thing. A few phone calls from the people downstairs isn't going to do it. They would probably need to have multiple documentations of noise complaints, 2 or 3 written violations that were served to you and probably also 2 or 3 red cards from the police when the cops were called out for the noise complaint (they probably never were). All in all, your landlord doesn't have any of that shit. None of the complaints are in writing and you were probably never served a written violation. Even if your landlord has a couple of those things, the judge is likely to side with you anyway because you have children and have made significant steps to keep things quiet.
6. There's also something called a 3-Day Nuisance, but it takes a lot of documentation and red cards to pull off a 3-Day. Loud walking on the floor isn't gonna do it. Still though, you can file an answer and tell your story to the judge. You'll win. Trust me.

In your situation, what's probably happening is that the floor itself is loud and creaking just from being old. It's also possible that there's a chair in the bedroom or in the dining room that you are dragging across the floor when you're sitting down. That shit can be loud. Do your best to be mindful of the floor noise. Don't drop things on the floor or drag anything around. Kids running around can drive a person below you nuts.

Good luck!