Just a fellow pet owner here.. but I do agree with you on keeping the commitments we make to our pets when we get them
One thing you should do first and foremost (next comes the trainer) is get a proper crate. I would do it today. Make sure she can stand, turn around, and lay comfortably in the size you get, but not so big she would think she can potty on one end and lay in the other. When you get it home, put a pillow or something in it for her to lie in, and cover the rear 2/3rds and back and sides with some towels or a blanket. So if she wants to make the back of it her safe little "cave" it will feel like one for her.
Then leave the door open, don't make her go in.. but keep putting treats, food, and her toys in the crate until she is going in on her own. Just let her know that the crate is her own place and optional. A lot of dogs really appreciate having a private, safe feeling place that is all their own. No one bothers her while she's in the crate, don't reach in for her... it's her place to call a "time out" when she's had enough human interaction. I kinda suspect part of the issue for her is just too much human interaction for her personality in the way of kids wanting to play and cuddle, and not enough privacy. Look at her like a teenage girl
If she's in the crate and you want her to come out, tease her out with treats and calling to her.
Then you can work on shutting her in. You can let her out as often as you like (though never during a whining or barking session), but never use it as a punishment spot. This way you can close her up if need be.
Our 4 month BC really LOVES her crate. She takes her naps in there with the door open and always runs for her crate when she's feeling a little unsure of herself. Shes a really good girl but she does think she can herd the 2 little Pee-Shi-Poo puppies all over, and she makes some attempts at herding us before we herd her back
As for other options should you need them.... it might not be what you wanted for her, but if you cannot correct the issue completely, and seeing as a house full of children and her feeling the deep instinct to "herd" and thus correct them all, might be the problem... you could think about letting her be more of an outside dog. Maybe you as an older kid or mom or dad could bring her inside when the smaller kids are asleep and designate a sleeping area for her, like her crate, or the kitchen or something (with a baby gate closing it off?) so she can sleep in comfort but not be part of the higher house activity during the day?
Do of course get the trainer asap too! But I would get the crate while I waited to find one!

One thing you should do first and foremost (next comes the trainer) is get a proper crate. I would do it today. Make sure she can stand, turn around, and lay comfortably in the size you get, but not so big she would think she can potty on one end and lay in the other. When you get it home, put a pillow or something in it for her to lie in, and cover the rear 2/3rds and back and sides with some towels or a blanket. So if she wants to make the back of it her safe little "cave" it will feel like one for her.
Then leave the door open, don't make her go in.. but keep putting treats, food, and her toys in the crate until she is going in on her own. Just let her know that the crate is her own place and optional. A lot of dogs really appreciate having a private, safe feeling place that is all their own. No one bothers her while she's in the crate, don't reach in for her... it's her place to call a "time out" when she's had enough human interaction. I kinda suspect part of the issue for her is just too much human interaction for her personality in the way of kids wanting to play and cuddle, and not enough privacy. Look at her like a teenage girl

Then you can work on shutting her in. You can let her out as often as you like (though never during a whining or barking session), but never use it as a punishment spot. This way you can close her up if need be.
Our 4 month BC really LOVES her crate. She takes her naps in there with the door open and always runs for her crate when she's feeling a little unsure of herself. Shes a really good girl but she does think she can herd the 2 little Pee-Shi-Poo puppies all over, and she makes some attempts at herding us before we herd her back

As for other options should you need them.... it might not be what you wanted for her, but if you cannot correct the issue completely, and seeing as a house full of children and her feeling the deep instinct to "herd" and thus correct them all, might be the problem... you could think about letting her be more of an outside dog. Maybe you as an older kid or mom or dad could bring her inside when the smaller kids are asleep and designate a sleeping area for her, like her crate, or the kitchen or something (with a baby gate closing it off?) so she can sleep in comfort but not be part of the higher house activity during the day?
Do of course get the trainer asap too! But I would get the crate while I waited to find one!