Disclaimer: I'm not great at hockey so take my advice with a grain or twelve of salt. I may or may not have any idea what I'm talking about.
For you the things that stick out like a sore thumb are your hands, your balance on the follow through with the wrist shot and your lack of utilizing your body to generate power.
Hands: Your motion starts well with your hands out in front but when you get to the snap part of the shot your top hand goes wild. Watch this whole video, but pay special around 4:39 when he shows how you want to pull back with that top hand in the middle of your motion:
Link 1. Notice how his top hand gets pulled back into his stomach almost? Your top hand goes sailing over your shoulder. It has no business being up there for the most part. There's times you might want to do that to help aim a weird angled shot or something but for the most part that's all bad. Keep your hands low and in control. Also, on the follow through make sure to roll your hands over so the toe of your stick is pointed sideways or almost down, not up at the sky. Rolling the blade over really corrals the puck during the release and lets you put it where you want it to be. If you get that down it'll increase your accuracy. That goes for both the wrist shot and slap shot.
Balance: Your balance is off for both the wrist shots and slap shots but definitely more of a problem on the wrister. When you release the puck you stand more upright and seem to lean backwards a little bit. You're wasting a TON of power by doing that. You want to drive forward into your shot, not away from it. The video I linked speaks about the proper balance and weight transfer for the wrist shot so be sure to check that out. Here's a good video on the slap shot motion and weight transfer:
Link 2
Power: Lastly, to maximize your shot power you'll want to work on incorporating all the muscles at your disposal to generate all that power for the shot. It looks like you're mostly arms and shoulders on the wrist shot. The slap shot doesn't look bad but there's room for improvement. Work on using your arms, shoulders, stomach, hips and legs to all generate power and find out how to make them all work together for a big release of energy into the puck. Drive with your legs, explode with your core, power through with your shoulders and snap with your hands. Pretty much every "How to shoot" video on YouTube will discuss this so check those out.
For her, it's more of the same but slightly different.
Hands: Get your hands out in front of you during your wrist shot. When your hands are in that close to your body you're stealing mobility which hurts your wrist shot greatly. Hands out in front lets you flex the stick more as well as lets you pull that top hand back to your stomach while driving with your lower hand for a nice explosion of power. Also, after you release the wrist shot keep your hands more in control. Your bottom hand tends to swing through the shot, which is good, but continues upwards until it's level with the top of your head. Keep those hands low and snap hard at the target. You should be pointing at your target after you release the puck, not up at the sky. Also, roll those hands over. On the follow through the toe should be pointing sideways or slightly down, not up that the sky. That goes for both the wrist shot and slap shot.
Balance/Power: Your balance looks like a pretty good place to build from but you're definitely not using your weight transfer to your advantage. For your balance you seem to be steady all the way through which is good. You start and end well balanced. Aside from that bottom hand on the follow through your body doesn't do anything too wild. However, your weight transfer is a different story. It looks like you start strong, driving off your back foot but you never really transfer that weight over into your front foot. It just dies somewhere in between. Let that power drive through your back leg and land hard on your front foot letting all that power explode forward, don't let it die in between. Same thing with your upper body. You start leaning into the shot well but as you release your chest just stops dead in its tracks and you stand up just a tad. Lean into it, drive your upper body forward into the shot.
Hopefully this helps some.
.
. I didn't expect such a long answer. I'll try what you said in a second video, and I'll post it here. I have to move somewhere else though, I nearly hit a window of the house in the background today while taking shots.
