This has been posted before, but here's an interesting article on using the gopro for simple underwater video production:
http://www.divephotoguide.com/underwater-photography-special-features/article/shooting-underwater-film-gopro-indonesia/ As mentioned, even with a housing mounted cam, you really don't want to be filming the whole dive though, sounds like a logistical nightmare to get something useful out of the footage, especially if not shooting with intent and snapping strobe-lit pictures during the dive...
Going for roughly 10 to 30 second clips (+handles), and up to one minute max if you want to capture a specific behaviour in more detail, all shot in between your still shots, sounds more reasonable.
Having a point and shoot cam at the ready on your housing means that wouldn't need to change anything on your primary camera setup for stills, wouldn't be using up its the battery (video really shortens battery life), framing should be relatively easy, and the footage is nicely stabilised.
Image quality will surely be better on a DSLR, but it also depends on what you're going after in the end.
Here's some basic tips on action cams for UW use that might also be of interest (I personally don't subscribe to everything said there, and really not a fan of the word "cinematic", but it's a good introduction to a less "action-focused" use of such cams, for those of us who don't really "want to be heroes")
The original post described wanting to:
- shoot occasionally, if a rare encounter/behaviour shows up and DSLR lens aren't a good fit, then maybe capture a video at less than 25m depth
- occasionall, record a family video when kids snorkel
- occasional (maybe) shoot some vlogging videos
In this case, why not play around with a cheap housing-mounted action cam (GoPro, Paralenz, Sony...) for maximum hassle-free flexibility, shooting in ambient light in between still shots, to get a feel of what you would be doing with the clips, and the post work involved for editing and colour correction.
Then maybe going for lights which you can keep as you upgrade - and eventually, if you want to dig deeper, going for good video-capable compact or a direclty something like a GH5 or Sony MFT and sharing the still/video workload?
Regarding wide angle GoPro-style cams and ambient light, it also depends on conditions, what you're filming and the kind of result you're going after.
In many locations, unless you have dedicated video lights powerful enough for wide angle even in the shallows, you can get acceptable results by shooting in a flat profile (limiting the adjustments the camera will try to do in terms of white balance and colour profile on a gopro this is done by turning on ProTune). You can white balance in post, but not UW.
Your footage won't pop without lights, but you can definitely avoid colour casts, and if the focus is on the behaviour or the experience, it can work.
Beyond the flat colour + WB profile setting on the action cam, on the GoPros you can also manually set the ISO (or leave on auto with a set minimum and maximum ISO) and also shutter speed, but aperture is indeed fixed.
Main issue with the GoPro 5 up to 9 is the increased distortion in their not-as-wide "linear mode" fov, compared to the GoPro4's medium fov which was fine. The distortion is probably used to the stabilisation processed introduced - it's quite ugly on the sides at the slightest pan and the change also killed the possibility of using close-up lenses efficiently.
On the TG5/6 you lose the shutter setting in video, but can set aperture to some degree and can also manually white balance underwater - sensor size is identical on TG and GoPro, but as previously mentioned, unless going for closeup (macro) video with lights, I wouldn't really bother with the TG for video for its bulk, hunting autofocus, weaker colour science, stabilisation and poor battery life when shooting video...
Shooting in identical conditions, I prefer the results I got native wb on a GoPro white-balanced in post gives better results than Olympus' UW manual white balance.
This here is shot on recent GoPros, mostly in ambient light, in the shallows
These are shot in ambient light in tropical locations, 0 to 20m range, UR filter, flat settings
If shooting mainly in Australia's more temperate and darker waters, ambient light might not be so much of an option though...
There's some really sound suggestions in this thread.
I'd just add that it really depends on what you're going for with the video footage.
If it's too complicated to simply use your DSLR setup as-is for such purposes, a (pair of?) housing mounted action cam - that you can get real cheap second-hand since these things are really tough - if set-up and used efficiently, sounds like a good way to get some footage to work on, and then building on from there, according to your needs as they develop.
