Mark Romero 2

You might get lucky finding an Olympus E-M10 III or Panasonic G85 secondhand for near ish to your budget?

Otherwise go for the older Olympus E-M10 II which can be found even cheaper.
I remember filming with my a5100 years ago and it would overheat after every take! So very frustrating

Agreed... for some purposes. But if the intention is to view on a phone or iPad type device in a casual and fun environment then, yes, the quality is absolutely there. 
I had mine on the snow earlier this year - initially I thought it was dreadful and was going to bin it. But my wife thought it was fabulous and watched the fun rather than the banding, dubious stitching (at times) and any number of other limitations (features?). 
The ability to let your audience reframe is astounding and produces a genuine immersive experience. 
I think it’s used by Sky Brown (who must be the coolest person in the world) in her BBC sport video.

I think its great for making little 30 second pieces from using the re-frame function in the app. To be able to make something interesting with multiple angles from basically just being stood there holding it makes it a great holiday/event camera as far as I'm concerned.
 

That would be a great solution for a reasonable person.
But it is my wife we are talking about here...

That would be a great solution for a reasonable person.
But it is my wife we are talking about here...

That would be a great solution for a reasonable person.
But it is my wife we are talking about here...

Ok, firstly, thanks all to everyone who has chipped in.
I guess I should have clarified something about this.
My wife does travel a lot for business and in the past she used a Sony a5100 with the 16-50 kit lens Instead of her cell phone).
I think the MAIN reason that she used the a5100 instead of the S7 she owns was... she believes that she needs a "real" camera to achieve her artistic vision.
Seriously: I try to show her videos on youtube of cinematic footage taken with a smartphone and she ain't having it.
Now, if you know me well (and, thank your lucky stars that you DON'T know me well), you would know that I HATE spending money on things that I don't need / won't get used.
So believe me that I have Anti-GAS; I mean, I have been asking people about an upgrade from my a6500 on this forum for two years now, and I STILL use my a6500 and haven't replaced it with anything. No a7 III, no Z6, no X-T3, no GH5, no EOS R / RP.
So, anyway, I would just have her use the a5100 (since it is just lying here collecting dust, and since she used it a lot for photos in the past), but for video those things overheat in the mild San Francisco weather in about 12 minutes. I am sure they wouldn't last half that in Morocco.
Now, I could get her an a6000 as @Kisaha suggested, but I am pretty sure she will appreciate the flip out screen and the IBIS a lot more than the aps-c sensor of the a6000.
I think a mic input would be pretty important, too. a600 doesn't have one, but it could work with a proprietary Sony mic that uses the hotshoe to transmit the audio from the mic to the camera.
 

Use her phone and be done when it! This is 2019.

how a camera you use professionaly isn't adequate for holiday photos and videos?!
Do not waste any more money. The a6000 is good if they want 1080p (and they should) and the other if they shoot 4K.
Use the PZ or the 18-105. They certainly are small cameras - which is good for travel, and they will shoot short videos, do not see overheating being an issue for not critical work.
As you put it, these cameras do not even worth 450$! And they probably do not. The a6300 is 670€ new here.

For all of the specs that you are after @Mark Romero 2 at that price point, its difficult to look beyond the FZ1000.
If you can up the budget and hunt around for a deal then a used FZ2000/2500 might be a good route because of the internal ND.
If you don't mind losing the mic input then Panasonic do compact form factor versions of their 1" cameras (TS100/TZ100) which might be more appropriate for travel (the FZ hybrids are pretty bulky) that also have the touch screen option. They can also be persuaded to shoot in Cinelike D if you know the right people  
The Olympus is a good option if you can budget for the lens but again you will lose the mic input.
An alternative to the Olympus if you were OK with going with an interchangeable lens system would be a used G80/85 that you could get for just above the budget and would get the mic input, IBIS and also an articulating screen which might be important if your son wants to do vlogging/selfie stuff.
A completely left field suggestion would be the Insta360 OneX as it really is a great travel video camera option in my opinion if, as has been suggested, the bulk the stills shooting will end up being done with a cellphone. With a bit of shopping around you get one of those and a used Panasonic LX100 which would be a great combo if more serious shooting is also required. 

Non-techie types do like using their phones, but "there is no zoom" is also something non-techie types who have a bit of interest in photography understand and care about.
Don't confuse people not knowing about cameras or tech with people not knowing about what makes a good image or what they like.  We are drowning in photos and video and therefore live in the most visually literate time in all of human history.
When in doubt, go for usability and durability, then just tell them to shoot everything and not worry about the camera.

I actually liked the FZ300 a lot when I owned it. The added bonus of the constant aperture zoom and CineLike profiles were a bonus.

Don't you have an a6xx camera? These are the 450$ cameras of today.

Thanks for the test. Looking good so far. Looking forward to any more DR tests you or anyone else can provide.
Curse you @Andrew Reid as I might have to buy a Z6 now... Thank goodness the preamps are so bad on the Z6 that I have held off buying it. Plus I can't really think of a good B camera to the Z6 (besides another Z6).

P4000 = GTX 1070
2x GTX 1070 = 1x Radeon VII
It is cheaper to buy another nvidia card, the performance will be almost the same.
But it's highly depends on card support, right now i dont think Radeon VII has full resolve support.
Unfortunetaly neither of these options will give you 1080 24 fps rendering while using Temporal NR (Better) with 5 frames averaging. You will get around 20-22 fps

Unless there’s a 4 or 5 before that 0, then I don’t want to hear it. Lol. Jk.
Consider yourself lucky...
• You don’t have to be in your 20s anymore.
• You know yourself way more than you did 10 years ago.
• And as Bioskop said, you never know what will turn the corner...
With the voracity and ferocity in which you made your short film, you’ll probably have a studio deal by the next time a 5 is your second digit.

Continuing with the Gravity Falls theme from @Ingerson:

You need to tell me what your address is so that I may catch the camera when you throw it out the window.
But as BrunoCH said, check whether your Saramonic has Mic Level Output or just Line Level Output.
Can you plug headphones in to the Saramonic output and hear the sound clearly? Then that would be line level (I think).

No no no no...  RAW goes in, COOKED comes out!

How much Dynamic Range does your toaster have???
Jeez, no kidding. I get about 8 minutes of video before mine overheats.

How much Dynamic Range does your toaster have???
Jeez, no kidding. I get about 8 minutes of video before mine overheats.

If you are ok with a green tint on your toast, I can loan you my Sony a5100. Great affordable toaster.

I like SLog2 on the A7III but just wondering if HLG3 would've helped in this situation? I don't own an a6500 so I don't know if it has HLG.

You need to post in this forum more often. You always have something helpful whenever you post here.

You need to post in this forum more often. You always have something helpful whenever you post here.