Ya, agree that the red sex links can be bossy birds with other chickens, they usually want to be in charge. I think it is the RIR or NHR in them, they are sweeter than RIR especially, but they retain some of the want things to go my way personality. But boy is Mickey Lou 04 right that they generally are good with people, they know where their treats are coming from and who they should be buttering up.
Think your red just need to get used to the chick, time should take care of that. I just meant with letting them interact (with supervision of course and the chick in a pen) outside if you had a fenced in area might be a better option if red is being a witch to the chick since it should give her other things to think about and she won't obsess about the chick being there. But it sounds like she is getting used to her, it will take some time, no need to hurry things along, especially since the chick is still so young.
Spending the extra time with her supervising her outside is good anyhow, should make her friendlier and even more of a pet, though it doesn't sound like she needs much help in that regard. Looks like your mom knew a good photo opportunity when she saw one, bet she will have plenty more. It still amazes me how different chickens are, even ones of the same breed. They are a lot smarter than you would think also, I swear some of them can out think the dogs.
I would guess your Wy chick will get bigger than red. I have mostly BLRW but I think every Wy I've had in any color has had has pretty much been bigger than the red sex links.
Your coop is cute, it's a very nice set up, looks like you are all ready to start collecting eggs, tell red to get going.