Hi Erin, you can really go down the rabbit hole on this and there are many options to consider. I spent my younger years in a household with 2 adults + 4 kids so I know where you're coming from with negotiating shower access, etc. I will add my own two cents and then let others add theirs. I'm going to assume that your house doesn't use a boiler for home space heating, which would change things, so please let us know if you do!
First, you should be able to meet the needs of a 5-person household with a single water heater unit. You just need one that is properly sized to your family's needs.
Second, before doing anything else, see if you can increase the performance of what you've got. Have a thermostatic mixing valve installed, and explore adding a drain heat recovery system. Either of those upgrades can substantially increase your hot water supply, and both will transfer over to your next water heater (if you still need one).
Third, if you do need a water heater capacity upgrade, the energy supply type really matters. In your situation, gas will definitely provide much better performance & lower monthly costs. But if you have only electric available at your house, then it gets really simple. You just need a lot of tank storage. With 3 kids, probably at least an 85 gallon electric tank. (Or two smaller 40 gal electric tanks if installation space isn't available for a big tank). Electric tankless is a poor choice for multiple reasons.
Finally, if you do have gas available, and you're shopping for a new system, you'll need to decide on tank vs. tankless. If you call plumbing contractors in your area you may get a "hard sell" on tankless. Tankless heaters have some benefits -- but they also have some drawbacks.
Often when you get a quote, the first person who visits your house is actually a salesperson. That salesperson may give you all the benefits of tankless and make it sound like the best thing ever, while glossing over or simply omitting the drawbacks. If you find yourself in that situation, do your own research, and please come back here and ask questions. Make an informed decision.
Good luck!