My parents, in their 80's, live in a gated retirement community park, we want to go visit them, my husband I are 60 years old, but we have just been informed that if we stay longer than 72 hours, we would have to pay $20.00 a day per person for each day we are there. They live in Arizona and we live in North Dakota. My Mother has some health issues and I was going o go down there to assist her for a month, but we can't afford those rates. Yes they said family is charged too, as in meaning us as her 60 year old children. Even if we were caring for her.

Is this the norm, when people own their own home in these gated communities, and now that my Mother is elderly and I have to pay to visit her?

Yes, it's within the norm, and it's legal. Extra residents cost the whole community in outside spaces, parking, water, sewage, trash removal, pools and tennis courts and other sports or common areas.
It may be time for them to move nearby. I would visit alone, and pay just the 20/day for about 10 days, while you sort out other options. Maybe you could arrange a 'house sit' in another unit in the park or something.

I wouldn't necessarily say it's the norm, but its certainly not unusual. Many of these senior communities try to limit costs and long term guests do increase use of resources over plan. Frankly, $20/day is not a huge amount and a hotel will cost you much more than that.

But the biggest point is your parents agree to these restrictions when they purchased their home in the park.

I agree, while perhaps most do not have such rules, it is common for others.

Assuming ages, if one is going to live there long term, to have them added to the deed and become a residence there also. But if parents are going to need more closer care, perhaps time for a new home.