Welcome back to diving!
The hose on the second stage felt like it was trying to pull the reg out of my mouth - like pulling out on the right side.
The hose was too short. You can buy all kinds of different lengths of hoses, although not very relevant when talking about regulators you don't own.
That said, you can sometimes get a couple more inches of hose by having the scuba-tank a little higher on your BCD, so the regs are right behind your head, and then rotating the tank or regs so the hose of your primary-2nd-stage come out at a 45-degree angle right over your shoulder.
(I may have employed this hack once or twice, or 10 times)
If they were your regulators, you could also attach a regulator-retainer necklace. There are some DIY version using a short length of bungie, or about $10 for one made of silicon.
Everything seemed good skills-wise, not that much was needed. Buoyancy was ok, not perfect.
That's expected. If you start diving more regularly, you can start working on that.
but trying to fin like the DM (modified frog kick, I think) will take practice.
I'm much more experienced than you, and my attempts to do Frog-kick so far have failed. I'm going to learn it soon enough .... I hope!
And I was getting low back pain, particularly during the second dive.
I'm not that old, and if I'm not careful, my back will hurt a little after scuba-diving.
When you have your scuba-equipment on, you have something like 45lbs on your back (tank + air + weights), where you're not used to carrying it. It's somewhat similar to moving heavy boxes safely, back straight, no twisting, use your legs, and similar "rules."
Any sort of
twisting is what hurts me the most. Specifically, be careful when standing up with your gear, or climbing a ladder. Once you start rotating, the momentum of the tank wants to continue rotating. Waves moving a boat-ladder as you try to climb it with a bunch of weight on your back is a recipe for back-pain! You can wait for the waves to pass, and also be careful to ensure you're not twisting a bunch.
This is perhaps getting very far ahead of today, but if you want to get back into scuba seriously, but the back problems remain, you should look into side-mount. Essentially, it's diving with 2 tanks, 1 on each side. The advantage is you can carry the tanks separately from the rest of your gear, clip them on in the water, and go. You can also use smaller tanks too, because after-all you have two tanks. There is quite a learning curve though, and the classes can be a little pricey, but it's something you might want to be aware of for the future.