2015 prius plug in EV battery drains too fast

A couple thoughts.
The first one being that it goes back to EV mode every time you shut off the car.
Another being that there's no electric heater but it will still try to use the battery if in EV mode. So if what I'm hearing you say is that you started out in EV mode with the heater on then yeah it might take a little longer to warm up and you'll be using gas and battery.
Also, the battery range is highly variable. If you were driving at like 55mph or faster or anything involving uphill it would be really unlikely to reach 10 miles.
If you're out on a nice day with no heater or ac needed or other weather to deal with and just gently driving on flat streets at speeds up to 30mph then you can probably get more than 10 miles.

 

drive history plays a big part in how the car drives. You're just gonna have to learn how the car behaves and with 159k that's a lot of drive history you don't know about.

 

Adding to the above ideas…
Driving conditions can play a large part. If the temperature was below 50-55 the air becomes dense enough to lower the efficiency.
If the roads were snow or sleet covered, that takes more energy and can lessen your range.
Have you checked the tires? If the tire pressure is low, that will lower efficiency as well.

There are other possibilities, but environment is one of the easier ones to monitor.

 

What reference are you getting that info from?
I can't say I've seen that. The only thing relevant I've seen is that when the 12v battery is disconnected for too long the engine sometimes seems to need a little bit to get running back to normal.
The range listed for the battery adjusts pretty quickly. I can get it to tell me it's empty in about 6 miles, or get it showing almost 20 miles.

 

Plus - there's not all that much discussion around here about the PiP currently, like there used to be before gen 4 was relased in 2016 or 17 for the Prime. And trying to get a handle on how the PiP behaves with all the current discussion about Prime is hard to impossible.
Prius EV/HV modes are a learning process. I started plugging in in my/our 2014 PiP and I'm still learning new things about Prius EV/HV.

Example: I have almost 100ft rise in the first 3/10s mile to get out of my neighborhood. If I drive slowly snaking around the neighborhood roads I can go about 3 miles before I have to climb that 100 foot rise. After 3 miles at sub 30 mph speed the cars been warned up for about 2 miles in the summer and is almost warned up in winter. Although when I have to take that 100 ft rise mpg and or EV range drops like a stone.
The main road I get on after that initial 100 ft rise goes down about 200 ft in 3 miles in one direction, but in the other direction, coincidently about the same distance (3 miles), it continues to rise to one of the highest points in the city, which is up another 300 ft or so from where I get on the road. And the speeds on that road are much higher 45 - 55 depending on if it's rush hour or not.

I can tell you from experience the car likes it a lot more and mpg / EV range behave a lot nicer, after the cars warmed up before the car has to climb up hills or merge into rush hour traffic, etc.

 

Levi to understand more about how the Prius or most any other hybrid works one has to pay attention to a lot more things going on than just mpg and EV range. And have other like minded owners offering their experiences to evaluate. Most hyper milers on this forum agree or at least used to agree that the prius driving history data stored in the ECU effects how the car behaves.
It's not something that is really noticeable to people that drive the same way all the time. It also doesn't mean that just because my car drives this way or that way, your car is also going to drive the same way under very similar conditions . The variations in behavior are wide. And if there are 2 daily drivers of the car the differences in the cars behavior become much more pronounced, especially when the driving styles are different.

 

you're not going about it the right way. levi may be right, perhaps you were in ev mode on the way home.
if you're in hv mode, the battery should not drain more than 20-25%, so maybe 10 miles or so left when you got to school.
the other thing is that 13.6 is not your range, it's an estimate based on past ev driving. once you have established some ev history, as vvillovv says, you'll have a somewhat more accurate ev range estimate after you charge up.
but it is still just an estimate, and many variables can affect it, like temp, rain/snow, topography, driving style, speed, and etc.