It is absolutely best to see turtles in Akumal Bay on your own (not with a tour).
You can walk out as it's shallow and the turtles come in close to the shore where they feed.
You can see little silvery fish a foot from the shore in a depth of 1 foot of clear water and this usually encourages the kids to look for more.

If you go out early in the morning before the tours arrive you will see more turtles, feeding and there will be fewer snorkelers to bump into. The water will also be less churned up and the visibility will be better.

We've never done a tour but have seen many of them arrive at Akumal Bay (this is when we get out of the water!). Our kids were younger than yours when they first snorkelled and took to it like ducks to water. My daughter was barely 8 and at 10 she did her first scuba dive at Akumal Bay so I encourage you to try doing this on your own first.

Get your equipment before you go and try it out in a local swimming pool or even in your own bath tub to get the kids used to using it.
Make sure you buy a snorkel vest for the kids if you think they will tire easily, are not strong swimmers or will want to be in the water a long time. These let you float without effort and are great for beginners. I use a noodle while snorkelling but it might take a little more getting used to than a snorkelling vest (floatie)

You can also walk out in Half Moon Bay to snorkel but will need reef shoes as it's rocky. I've almost trodden on a large ray about 10ft from the shore in less than 2 foot of water.

Yal Ku lagoon is like an aquarium and a very easy place to begin snorkeling!

Cenotes are sink holes. By underground do you mean in a cave? You will see fewer if any fish in the caves.
Maybe the best bet for you is a tour to Xel Ha. You can snorkel with their equipment, there's a cenote, a lazy river and ziplines into the water plus all food is included. It's a great day out!

By the way I forgot to add..
Please, please tell your kids to keep away from the turtles and don't touch them. Another reason I dislike tours is that the mass of snorkelers stresses the turtles and drives them away.

Thank you so much for the tips! We will do turtles earlier in am without tour...our kids are very ecologically sensitive and know about safe distances from animals in their natural habitat but thank you for the reminder!

I heard the reef is about 300 feet out for snorkeling...is a boat tour helpful?

Honestly you do not need to go out to the reef, you will see lots of fish, rays, turtles in 100 feet out of less. Go out from in from of Lol-Ha and the Akumal Dive Center. You can also snorkel over toward the north end and see if you can find the cannons. Good idea about the snorkeling vest.

Check out the wind conditions in Half Moon Bay, it is rougher there when it is windy and sometimes near the center of the bay there can be a rip tide at times. Wear water shoes to protect your feet from the coral and sea urchins. This will not be a problem at Akumal Bay.

Please do not touch the turtles or stand on the coral and also please do not feed the fish, as they can bite.

Have a great time, I'm going in May and staying on HMB myself.

In Akumal Bay, you will see 2 foot long fish in knee deep water. There are fish everywhere. To see turtles, you will need to snorkel out about 300' feet or so, where the water is about 8' deep. The bay is generally quite calm, and it's easy to get out there, even with children. As far as where to go - don't worry, you will see snorkelers over the turtle grazing spots.
A few tips - ALWAYS have everyone wear a vest. I believe it's now required anyway. If it's a very windy day and the water is a little choppy, it may be trickier for the kids - wait for a calm day, especially if it's the first time. If you feel a little uncomfortable going out with the kids, you can always go with a tour group. They go out every few minutes from the dive shop. You can also go out in one of the boats, but it's really unnecessary.
Definitely snorkel in Yal-Ku first, it's so easy there, and the kids will see thousands of fish. The shallower parts of the lagoon have the most fish, there's not much to see going out towards the ocean side.
Half Moon Bay is a bit more difficult to snorkel due to the rocks, sea urchins, etc. It's usually a bit choppier also.
Cenotes are crystal clear pools in the jungle, often they have caves running into them. An easy one for kids is Casa Cenote, which is just south of Akumal on the ocean side. There are also many of them on the road to Coba.

Thank you for all of the help...I wish we had gotten a condo on Aukumal Bay not half-moon Bay...it seems the snorkeling will be better for us at Akumal Beach... Live and learn. Hopefully we can rent bikes and make the trip over a little quicker.

We've been to cenotes in caves close to Chichen Itza and they were amazing because they were underground...otherwise the cenotes we've been to are rather dull. Was hoping to find a similar cave spot for my youngest to see as she was too small to remember the others.

As an aside...if anyone wants info on Isla holbox we've been going there for 10 years and will be back this spring so will see all the new changes on the island. Great VERY quiet spot for young kids...no snorkeling though...too cloudy. If you get the chance to go in February for carnival it is very unique small town Mexico experience.

thanks for all the help!

boconnell, I hope I didn't turn you off to Half Moon Bay. We have stayed there many times, it's a beautiful spot, and blissfully quiet. You can certainly snorkel here, but it is trickier than Akumal Bay. If you hunt around along the beach, you can find places to access the water without walking over coral, rocks and such. Don't miss lunch at the Buena Vida at the south end of Half Moon Bay, where you can dine with your feet in the sand, on a swing, or up in the crow's nest!

Zootsi , is right Half Moon Bay is lovely and just look out for the sandy entry places.

Ideally you should rent a car to get around as in the heat bicycling and walking any distance is tiring especially for young children. We walked to Yal Ku lagoon once when we only had a car for part of our stay. Never again!

There is plenty of parking near Akumal Bay if you avoid the busy periods. Have lunch at the Turtle Cafe or other restaurant near by and your parking is free.

You should be fine, Half Moon Bay has a nice selection of condos, the only condos on Akumal are Las Casitas - they are two bedroom with their own special beach but unfortunately no pool. You can rent bikes from several places including Vista del Mar near La Buena Vida, or rent a car, there are also golf carts for rent inside the reception for Hotel Akumal Caribe, cost is $40/day plus deposit. If you eat at La Buena Vida, try the Bocadito platter to share and the Cheyenne tacos.