Advice can be a dangerous business, so just a few brief thoughts. It looks like neither of your above two candidates have optical (as opposed to “digital” cheese-ball quality) “zoom”. The Polaroid is (to me) more attractive (only because it uses 2 non-proprietary AAA batteries) - but other than that, both look pretty close to a frustrating waste of money. Looked through several on-line “reviews” of cameras for kids. Almost all of the items offered looked goofy and/or crappy in terms of quality (and one can pay up to ~ $160 for that).
I myself would probably be tempted to spend around twice as much (~ $88) on something of a “real” (while still inexpensive) entry-level camera with optical zoom and more serious, versatile in being adjustable, and probably durably useful, photo/video functionalities.
This item is the only thing (which I came across, anyway) that seems more likely to be worthwhile (at $88):
20 Mpixel (interestingly, CCD) Image Sensor;
5x Optical Zoom, 26mm - 130mm Focal Length, F/3.2-4.4 lens (able to WA focus as close as 2 Inches);
2.7 Inch diagonal TFT-LCD View Screen.
Note that the “SteadyShot” image-stabilization is electronic (in processing, after the fact of recording).
A Review: https://www.lifewire.com/sony-dsc-w800-review-4589510
Sony Factory Specs: https://www.sony.com/electronics/cyber-shot-compact-cameras/dsc-w800/specifications
Amazon listing: https://www.amazon.com/exec/obidos/asin/B00I8BIBCW/ep0cb-20/
Sony cameras use proprietary battery-packs that are re-chargeable through the USB port - but a (not provided) external re-chargeable battery charger is required to externally charge batteries otherwise.
The level of care of a soft-case for carrying is wise - as the lens-covering assembly (the small movable metal “leaves”) is not necessarily impervious to dirt/dust entry, and failures surrounding that mechanical assembly (from what Sony compact camera problems I have read about when considering purchasing Sony RX-series models) were the single most common Sony camera failure-mode that I saw being reported.