I think you have a bit of a flaw in there already.
If the scientist died, the girl would surely be on the run, wouldn't she? Wouldn;t she be hiding somewhere? Instead of just going to school as normal. I mean, she would be extremely upset at the very least, and not wanting to go to school.
Next, based on the premise, theres no reason to put the blueprints in a ring. Unless the fact that its a ring is somehow significant to the plot, it so far doesn't make sense to go that extra distance. Stories do best when simplified down to just the elements needed.
Finally, to be honest, so far your main protagonist doesn;t sound relatable. She is hiding these blueprints from her father, who was planning to SELL them? Nuclear secrets? That makes the father/scientist the clear bad guy in this situation, do something extremely immoral, and his daughter goes along with it.
And lets face it, if we're talking about the security services and a group of terrorists, they are NOT likely to do a whole "pretend to be students" thing. They'll just kidnap the girl.
If I can make a suggestion - refine it right down to basics if you can.
First, drop the terrorists. Instead, scientist works for a company, and they're doing something bad. He steals the files because he wants to give them to the authorities. That at least puts him and his daughter on the right side, and are more relatable protagonsists. The company send people after them, but so do the security services who are expecting the files. The moral dilemma is solved there.
Next, I would say either drop the ring notion, or come up with a reason why it HAS to be a RING, specifically.
Finally, drop the teams. Too many people confuse things, and would look REALLY weird if a large group of people suddenly start in a new school on the same day. Maybe one from each side, or one good character, and a small team of nameless villains whose names and backstories are unimportant, they just work for the bad guys. The easiest thing here is if they don;t even know they;re working for the bad guys, and are already in the school. maybe they're bullies, and are paid by someone to steal a specific thing from this girl.
And as a final note, its probably worth setting thes tory some time AFTER the scientist has died. Otherwise the griveing process will still be really raw, and would make the story seem less believable.
You'd have to explain exactly what was special about the blue print, or considering it's a low budget film you can just call it "the file" for the film. There's also no reason for it taking place in a school other than convenience for you. Why did he take it to the school? Did he have to attend a parents evening, or pick the daughter up from an after school detention? Does the facility not know he's stolen the blue print in the first place and he has to act as though nothing's changed so they don't suspect him?
To summarise, make the file and the company etc very vague. Maybe just call them "the company" or something. Create a reason for it taking place in the school, otherwise it will just look like you've shoe horned a government conspiracy plot into a secondary school. Are the terrorists still in the school looking for the blue print? Is it a bit of a White House Down sort of situation?
One more thing would be to make sure you watch lots of films that relate to this concept (White House Down, Die Hard, the ending of Leon) and look at how those films are shot and made. Then move onto small budget films like Green Room, Cloverfield etc and what they did to work around it. Green Room spent most of the budget on the gore and the effects to make it as shocking as possible, so Jeremy Saulnier made the story very simple to account for that, making it a very small and contained situation. You might want to think about that. The bigger your location, the more complicated the plot becomes as to why your characters find each other so quickly. Keep it simple, don't get carried away with extravagant action sequences because you don't have the resources to do advanced practical effects, or decent special effects. Avoid guns if you can, it might be tricky but good gun props are hard to get hold of and realistic bullet shots are even harder to produce.
Good luck!