Also, for a collie/aussie mix, 45 minutes when you get home from school might not actually be enough for a dog thats a cross between two high energy breeds. When you say collie, which collie breed do you mean? There are four of them and they can be quite different.
She is part Collie, as in Lassie. She probably does need a longer walk, but I'm scared that it will be too much for her joints. I've been told over and over again that heavily exercising a dog before they are at least one year old can cause all sorts of joint problems. I'd love to start jogging and doing agility with her as well, but her only being six months shoots that down. But for all of her flaws, she does walk well on a leash.
After the walk, she lays down for a little bit depending on what kind of activity is going on in the house (if me and just one other person are the only people here, she lays down and sleeps until dinner time, and then after a brief play session she is out again, but if there is a lot of people moving about, and with a family of seven that is quite often, she is still hyper and a pain in the rear). Generally she'll get a couple of fetch sessions coupled with obedience work, and maybe a short 10min walk around our field, before bed.

I didn't read all the post admittedly but where aggression is concerned and, especially with kids, it is much wiser to have a pet behaviourist come in person and see her with their own eyes around all members of the family and perhaps arrange for a visitor so they can see the dog with them.
It would be a struggle for me to afford a behaviourist. I'll do it if I absolutely have to, but I'm going to try and work it out on my own before doing anything. Not only would it be hard for me to afford, I can't find any in my area.

I don't carry around Bacon Bits in my pocket all day long either, but teaching new behaviors always requires heavy treating for the first few weeks/months and then gradually fading it out to mere jackpotting every now and then. If Chloe only gives up her objects for food, don't give up and assume that the food will become a crutch. Furthermore, you're right. You can use the play with the toy as a reward, but you can't work up to that unless Chloe understands 'Give' well enough. If she's getting too amped up and won't give up her toy, stop. Just stand there and hold the toy. She will stop trying to tug it from you and will stand there with the toy in her mouth. Say 'Give', treat, resume play. Eventually, she'll let go when you stop playing, and you can in turn use that to cement your 'Give'. It's doable and it does require a lot of treating, but, in the end, you have a dog who *wants* to give up her items. And if Chloe wants to give up her items, there's no more reason left for her to growl or snap at people.
This was originally what I was doing. It got to the point where she'd stop tugging the toy when I stopped, but she would NOT let go of that toy until she saw that I had a treat ready for her. Once she saw the treat in my hand she'd spit the toy and take the treat. If I tried to trick her by acting like I had a treat in my hand, she'd give me a look like, "Phhhh, ya right. I've got you figured out lady," and she wouldn't let go of the toy.