I can ask for Stone Shape, third circle, and seal an entrance, though the noise might alert the beast. If there’s two ways in and we don’t want her escaping, we’ll need to bring a second cleric, and hit both at the same time.

You'll probably also want a Dispel Magic, in case there's some kind of trap or warding at the entrance or a choke point, which takes up another third circle slot.

Spell slots are something casters have.
They come in different "circles" describing their relative power and complexity.
3rd means the next one after 2nd.

Three is this many fingers.

So we get up the cliff all sneaky, and then we all rush in and hit her really hard until she dies?

Then we figure out what buffs we want, so that the clerics can pray for them.

I can fit eight people in a Protection from Energy against the fire damage, that somewhat limits our party size if we want everyone under it.

We'll want to ensure everyone on the frontline can get past her damage reductions, and otherwise deal enough damage as fast as we can. We could try to prepare cold-damage attacks? But she'll might have Resist Energy herself to cover up her obvious weakness.

Since we know the beast can go invisible, we’ll want more than one countermeasure. Zarhbub can cast See Invisibility before we enter, and if we bring my wolf she could smell it out, but what after that?

She can’t attack without breaking the spell, and never attacking isn't a viable strategy so long as she's trapped. We don’t need to be too worried as long as we can hit back hard enough.

Ooh, can I be invisible too? That sounds fun.

She’ll have blindsense, and maybe See Invisibility herself, and in any regard if she attacks you first we’d be better off for it.

Let's go through the list again.

Eventually, Mother decides she's had enough of these brats.

She prepares to give them the speech.

Children, it is time for me to tell you the important things of being a dragon.

The world is vindictive and cruel to all who live in it, but as red dragons you are born to the highest caste and will come to stand above the rest. You come from a great and powerful line. Your mother, Arkrernux, is great great granddaughter of the great wyrm Daralathyxl, the most powerful dragon in all Golarion. But you can only reach his greatness if you reach his age, and that is no easy thing to do.

Survival must be your first concern.

What's a Arkrernux? What's a Daralathyxl?

They're names. Arkrernux is my name.

Do we have names?

Oh, right. She was supposed to give them names.
"Yes, you are Dergaix and Faumetun."

There, two perfectly good names. 

Can she pass a DC 60 perception check to hear the rather loud noise of stone being magically shaped, from 200 ft away through several thick walls?

1d20 + 23 = 36.

No, she cannot.

Wait which one of us is Dergaix and which is Faumetun?

I Suggest each of you sit still and be quiet until the end.

The DC is 16, but it's a very reasonable suggestion, so they take a -1 penalty.

They both have +7 Will saves.
1d20 + 7 - 1 = 16.
1d20 + 7 - 1 = 22.

Dergaix fails, Faumetun succeeds.

We can only beat her Suggestions like half the time, and if we pass she'll just use it again and also be angry about it.

So I'm going to roleplay like it worked for now.

Anyway, you are currently in a mountain in southern Belkzen. Belkzen is full of orcs who are likely to see you as a challenge to grow their names, so you'll want to avoid them for now. It does have some nice warm nesting spots but that won't be your problem for a while.

In the north of Belkzen is the territory of another red dragon family. Avoid it. There are also powerful dragons in a few other places like in Five Kings and west of us in Varisia. You'll want to avoid them too. You shouldn't even be thinking about claiming any significant territory until you're at least 400.

No, I'm only 130.