The advantage of pumps in general (tubed or patch) is that they can do much smaller doses and you can fine tune things in a way you could never do with pens. Which is quite good for children who generally need much smaller doses. For example, if you find her basal is too much at a certain point of the day but OK the rest of the time you can just change that portion and leave the rest alone (basal doses on a pump are set by the hour so you can change each hour separately and don’t mess with the bits that are working). Whereas once you’ve injected the long-acting insulin then you’re stuck with it at that level for 24 hours and it may work fine during the night but be not quite right during the day. However, it takes a LOT of work to set them up so that they are running optimally, and even then things change all the time so sometimes you feel like you’re constantly fiddling and never quite getting it right. They certainly aren’t an instant fix! Also, if you’re looking for some sort of closed loop system, which links to a sensor and adjusts basal automatically to try to keep you in range, they can’t be used on children under about 6 years old, which I think yours is? Because their doses are too small for the system to be able to adjust effectively.
If your daughter is shooting sky high after food that would suggest that timing is an issue, try doing her bolus a few minutes earlier to give the insulin time to get working before the food hits her blood stream.