I check my daughter in the night, usually only once though! When she was diagnosed aged 6 all the nurses, doctors, and even my mum (who has been type 1 for 50 years now) said it's not necessary to check at night, the hypo will probably wake her up. I find it doesn't though, when basal testing and since we've had the Libre (you can scan and see what's been going on with the blood sugars for the last few hours) it shows that sometimes she has been low at night for several hours and she doesn't wake up! So I've now fallen into the habit of checking her anywhere between midnight and 3 am, whenever I am awake, and if she's ok then I leave her alone for the rest of the night. Obviously if she's low I have to deal with it and then check again later, and occasionally I find her to be very high and have to give her a correction dose (not so hard as she is on a pump so I only need to push a few buttons). I want to keep her safe of course, but at the same time I don't want to get obsessive about it! It's easier now we've got the Libre and can just scan her, unless she's lying on the sensor and I have to roll her over to get at it, but even in the days of finger pricks I found that I could do it all without her waking up! She's 12 now, I guess there might come a point soon when she doesn't want me barging into her room in the middle of the night any more, and then we'll just have to hope she's ok, my mum has lasted 50 years with T1 without anyone doing night checks on her! (She was 22 at diagnosis though, didn't go through childhood with it)
I used to get really stressed about every low and high and why had they happened, sometimes you can see a reason for it and can perhaps learn a different ways of dealing with different situations, or occasionally you'll realise you might have made a mistake with the dose or the timing or something, but then other times there's no logic to it at all! Diabetes does have a habit of throwing curve balls at you, usually right out of the blue just when you think you're getting the hang of it! You could send yourself completely batty trying to get perfect numbers all the time though, and you have to enjoy life, so you do have to learn to relax a bit once you've learnt the basics. Finding the right balance can be hard though, obviously you want to do your best for them, especially when they are so young and have their whole lives ahead of them, naturally you want to give them the best possible chance of having a long and happy life, but without blood sugar numbers being the first thing you think about all the time! I found it very hard not to try to micromanage it all the time, but I think we are all a lot happier since I've learnt to relax a bit and not quiz my daughter about what her blood sugars have been doing the instant she gets home from school!
Are you carb counting yet? This means adding up how much carbohydrate is in your daughter's meals and adjusting her insulin dose accordingly, which gives her much more freedom to eat what she wants. If she hasn't long been diagnosed then maybe you haven't got that far yet, there is so much to learn that they try not to overload you with too much at once. But when you feel ready please do ask about it as it is a much better way of managing the diabetes, although it does mean that you can no longer just sit down to eat anything without doing sums first!
Pumps are brilliant, you can do a lot of things with them that you couldn't possibly do with injections, so you can fine tune the insulin doses much better and it makes it easier to deal with things like illness and exercise and so on. So do ask about them; they involve a LOT of work though, I sometimes feel like I'm constantly fiddling with my daughter's pump trying to keep her blood sugars as even as possible, and then I never quite get there

We got a pump 8 days after diagnosis, only because a trial was starting up comparing diabetes control with pumps and injections in newly diagnosed children. We had only 10 days to decide if we wanted to join the trial, so had hardly got over the shock of the diagnosis and were still just trying to get to grips with the basics of testing and injecting and how our lives had changed. Pumps were a completely alien thing to me, I at least vaguely knew what to expect with injections because of my mum. So I was not keen initially, but hubby persuaded me to go for it and we were lucky and got picked for the pump part of the trial, so then had to learn a whole new load of things such as how to "inject" with a pump, changing cannulas, refilling the pump, carb counting etc etc. OMG talk about brain overload, I think I barely knew what day of the week it was for a while and my brain definitely hit a wall and couldn't take any more in at one point. BUT it took me less than a day to see that the pump would make some things loads easier, so we stuck with it, got through the hard patch and have never looked back.
It's early days for you and it's all still a big shock, just hang in there, keep doing what you have to do, take as much help as you can get from the hospital and if you can get your mum and partner involved then it's probably a lot less scary than having to do it all on your own. It does get easier in time, honest! And keep asking questions, we are all very friendly here and were all beginners with the diabetes once, no question is too silly!