Hello @itsDEE4 ,
It sounds like your Contact Sensor “Placement” settings on your doors are incorrectly set as “Secondary Door” or “Window” (always immediate siren response) instead of set as “Main Door” (for delayed response if there is a Entry/Exit delay set at greater than zero seconds). So I’ll try to go a little more in depth and detail here (not to insult your intelligence in any way, but rather to “cover all the bases” very thoroughly), just in case you missed something or miss-set something incorrectly. 
Of the 3 available alarm modes “Disarmed”, “Home”, and “Away”, only two of them are Armed Alarm Modes capable of activating the alarm response & siren. The " Home" and " Away" Alarm Modes are the two armed modes.
Typically, most people set up their " Home" Mode with all their door and window Contact sensors enabled to form a ‘protective perimeter barrier’ around them while they are home inside. And they typically set up their “Home” Mode with their Motion sensors not enabled to allow their interior movements (which are still being detected) to NOT be used to trigger the alarm response & siren. That way, as long as you remain inside (not opening an exterior door and not opening a window) you are free to roam about without a Motion Sensor triggering the alarm response & siren.
When you depart the house and everyone is away, most people configure their “Away” Mode settings to have ALL Contact and Motion sensors enabled , thus detecting Intruders that trigger the ‘protective barrier’ and/or cause movement Motion inside (if they gained entry by breaking a window instead of opening it and thus not activating the window’s Contact sensor).
BUT, Ring designed the Modes so you can tailor both Armed Modes of “Home” and “Away” as you want. You can change your settings in each of the armed modes to have any combination of Contact or Motion sensors enabled, but you must have at least one sensor enabled. If you really wanted to, since “Home” and “Away” are essentially the same (just named differently for you to remember which is configured which way), you could have your Motion sensors used in “Home” mode and Motion sensors not used in “Away” mode, thus reversing their roles. So, Home and Away are both armed modes, named as such for your convenience in remembering how you set up your sensors in these modes.
To ** enable/disable which sensors** you prefer to have in each Armed Mode :
- Main Menu (the 3 horizontal line icon, upper-left-corner of dashboard) > then select “Devices” > Alarm Base Station > and then select the Contact or Motion sensor > Mode Settings > and toggle whether you want this sensor to trigger or not trigger the alarm in the “Home” and/or “Away” Modes > and finish by selecting “Save” upper-right-corner.
Now in your case especially, the " Placement" setting is important for your sensors. Once an armed Mode is activated, the “Placement” designation you set for each sensor will determine if the alarm will immediately go off or delay (for the time you set on the Entry/Exit delay).
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Contact Sensor “Placement” set at:
- “Main Door”: Uses delay Entry/Exit Time settings.
- “Secondary Door” or “Window”: No delay. Immediate.
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Motion Sensor “Placement” set at:
- “Entryway”: Uses delay Entry/Exit Time settings.
- “Room”: No delay. Immediate.
To set “Placement” for each sensor:
- Main Menu > “Devices” > Alarm Base Station > and then select the Contact or Motion sensor > select the blue “Gear” icon (upper-right-corner) > Placement > choose Placement designation > “Save” (upper-right-corner).
You set a Entry/Exit delay (most use the 30-seconds option) so you have sufficient time to arm/disarm as you exit/enter. On the entryways that you use, set Placement as “Main Door” (Contact sensors, and you can have as many “Main Doors” that you want to use, not limited to only one door). And any Motion sensors that can possibly detect movement at these entryways, should have their “Placement” set to “Entryway.” You can also have a time-delay Entry or Exit delay different for Home Mode and Away Mode.
To set Entry/Exit Delays for “Home” and “Away” Modes:
- Main Menu (the 3 horizontal line icon, upper-left-corner of dashboard) > Settings > at your Location select “Modes” > for Delay choices, pick “Home” and/or “Away” > scroll down to Entry Delay / Exit Delay and then select > Pick your desired time delay > “Save” (upper-right-corner).
So, if I understand you correctly, you want your kids to be able to come in during the day and use the PIN to disarm out of the “Away” armed mode, when they come in. And then you want them to re-arm the Alarm into the “Home” mode while they are inside. With your entryway doors having a “Placement” setting of “Main Door” and a Entry delay for “Away” Mode of like 30-seconds, this would enable them to enter with sufficient time to put their PIN in to disarm out of the Away Mode. Then, you should have set the “Home Mode” to a zero-second Entry delay time, so even though the “Placement” is “Main Door”, these entryway Contact Sensors will cause the Alarm to go off immediately, if this is your desired goal. Bottom-line is that you can use the above information to tailor the armed modes to react as you find best suited for your needs.
By trying to “cover all the bases”, I hope you find something that I wrote helpful in your case.