Kayak.

I'd sit on top kayak for those uses.

And to be not helpful to you, then I'd say SUP.

Given that I am guessing you're not out swimming on open sea when it's full on surf competition conditions then a decent volume SUP will be plenty stable and is way easier to get back onto if you have had an off. Remember you can kneel on them if there is a reasonable swell.

SUPs are slower than the kayak as well, so easier for the non swimmer to not get too bored whilst the swimmer is doing their thing.

Of course could go middle-ground and use the sit on top kayaks, whch if that's what was meant above then II take it back, we probably agree. But not a 'proper' kayak.

I was going to say surfski (which I have) but wasn't sure most would understand. Everyone knows kayaks.

+1 for a sit on top or ocean kayak. We've spent a lot of time on them since our girls were about your age and they've never once fallen out/off (jumped in many many times though!). Very stable, and faster and more manoeuvrable than a SUP, or at least less skill required to achieve speed/manoeuvrability, which would make them useful if you are ever in a scenario where you need to get to somebody in trouble in the water quickly.

I would think either a surfski or paddle board would work well as it doesn't take a lot of speed to keep up with a swimmer. Paddle boards are way easier to throw on the car and store in the garage. Both types of watercraft come in a bunch of hull speeds. Faster boards and skis are tippier (if that is a word) but are way more fun on flat water. You sort of have to figure out your use as you want as fast of craft as you need. Paddling a pig is not as fun as going faster, but for play stability has merit as well.
Some places will rent skis/boards for you to try and in some places there is a whole subculture of surfski/paddleboard competitions you can get sucked into. Both are fun to use and with kids playing in the water is always a cool thing to do. I don't think there is a wrong answer as there are so many variables out there.

I was thinking, perhaps, an inflatable paddle board for storage sake. We do not have a garage and live in the city...so anything that needs to be kept outside or trailer isn't an option. Does anyone have experience with the inflatable paddle boards? If so, what brands can you comment on?

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Ironman Lake Placid 2021| 70.3 Worlds St. George 2021

Seems like everyone is ignoring the request that you were going to have two little kids with you on this craft?? If so, then its the canoe, that would be the safest, easiest, and you could carry all the gear of a swimmer in the water and 3 more people pretty well...

If it were just you, then a stand up, surf ski, paddle board, sit on top kayak, sit inside one, would all be fine. Just a matter of what kind of workout you want to get too, as you will have this craft after she is done swimming too..

Yes, we will have 2 young children with us that will require a cooler of food and drinks. I will likely be doing a swim followed by my wife. switching spots with each other. We will also want to keep the kids entertained while we are doing this. I was thinking a wide inflatable paddle board could hold a cooler, etc. and we could just mainly use it for swimming while in lakes as opposed to the ocean.

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Ironman Lake Placid 2021| 70.3 Worlds St. George 2021

My wife has this inflatable and she likes it. She and her SUP buddies do sunset cruises with wine and fancy treats so it will definitely haul a small cooler and has tie downs to secure one. Very easy to transport and store. https://www.amazon.com/...=tower+paddle+boards I am surprised how rigid it gets when inflated - it is like a Zodak boat, not an inflatable pool mat.

I don't paddle but if you get a good inflatable, my understanding is they are as just as good as a rigid board until you start looking at high performance or racing boards. Perfectly fine for what you are contemplating (assuming your kids are not squirmy - a canoe or kayak is probably better for hauling little kids.

Two small kids and some gear seems like a stretch on an SUP. With wind anywhere but at your back, pacing a swimmer might be impossible. However, your storage constraints make an inflatable SUP about your only option. Inflatable kayaks don't seem to be as rugged as the SUP's and quality folding ones are very pricey and better suited to solo paddlers with limited gear.

You may have to only swim where you can rent a canoe or double kayak.

I've had two of my kids at a time on an inflatable SUP with a cooler and had no problem. I paddled from my knees and they were able to move around reasonably without tipping anything over. I believe someone already mentioned that it's likely easier to pace a swimmer on SUP rather than kayak/canoe due to speeds. My concern would be with child attention spans if you're planning long open water swims :-) Anything you bring on a SUP has a decent chance at getting wet or falling in, so if you're bringing toys or other entertainment that shouldn't get wet or can't float a kayak or canoe may be better.

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I would vote for an inflatable kayak. I have the Advanced Elements 2 person inflatable kayak. It can fit an adult and 2 children under 10 easily. It has decking to accommodate gear. It's not fast, but that's an advantage in your situation. Get the drop stitched bottom. It makes for a much more rigid boat.

We have a canoe, sit on kayaks, solid SUPs, and now an inflatable SUP - thank you Slowman and Xterra!
Unfortunately for your case you are looking for aspects of each of these and will end up with a compromise - you will have to decide what are the most important requirements and which you can do with out.

Canoe - good for carrying your cooler/kids, and can be most comfortable especially after a hard swim. If there is a decent wind and you are the only one paddling (your kids are unlikely to be much help) the higher sides can make for hard work. Getting into a canoe in open water requires a little skill. Storage and transport is obviously an issue.

Sit on Kayak - fishing versions have storage options but there won't be as much room for the kids. Easy to control in most conditions. Getting on/off relatively easy compared to canoe. Storage and transport an issue, unless inflatable.

Solid SUP - the larger versions have straps and space for a cooler - if kids are small enough they can sit on the middle and front (many larger SUPs rated to 250-300lbs). Kids have to actively sit - ie. you don't get the support that you do in the kayak. Getting on and off is easy with the wider more stable boards - almost like a mobile diving board. Easy to control unless rough, but then you just kneel down. Storage and transport an issue.

Inflatable SUP - most of the same characteristics as the solid SUP - except easy to store and transport. I was impressed with the Xterra board - I think it is only in rougher water that you would notice a significant difference from the solid SUP. Easy to pump up and very stable as long as you inflate fully.

It sounds like an inflatable kayak or SUP is what we are going to select in the end. We want something easy to store and take with us on vacations. It looks like the Advanced Elements 2 person inflatable kayak will be worth of coastal water ways and the SUP wouldn't be as seaworthy. It also has the added benefit of three seating positions, which would all for the kids to sit in the front section of the kayak one in between the others legs or even facing each other.

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Ironman Lake Placid 2021| 70.3 Worlds St. George 2021

We love inflatable paddle boards, you get the same benefits as hard paddle boards but easy to get around.

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