The pretty ones can't be trusted

Not much going on here these days!  It's quiet living.  Besides trying to attack the monkey sitting on the guest bed, Mia has been very well behaved.  She's super attached to her mom because mom takes her to the park and she Loves the park.  There's something about meeting all sorts of new dogs off leash that really makes her happy.  She whines in the car the entire way there (this is actually not good behavior) because she knows exactly where we are going and can hardly wait.  She still is kind of barky on occasion but is totally fine when we least expect it.  Perhaps her worst habit of all is that she still barks at kids - all the time.  At the park, if someone brings their kid along, she'll bark at them and jump all over them for a few minutes but then she'll stop and play super well with them.  I'm certain that she Likes kids because she'll be the only one in the park that will play with them while the other dogs just ignore them entirely.  It's bad manners for sure but since we don't have kids, or know kids old enough to practice with her on it's sort of something that we can't really work on too much.  Today, I picked her up at daycare and for some reason there were two kids there a 12 year old and a 10 year old and she barked at them the second she saw them [sigh] and then tried to jump on the little one of course.  I tugged on her leash and was just like, "she's really friendly, just really loud!!"  Luckily, they weren't afraid of her vicious bark.  What do I do about this?

This gate actually came with the house.  It's genius.  Our deck is sort of like a teenie tiny play area.  Unfortunately, she does need much more space to run in.  We really need a fence, but the idea of fencing in our entire back yard is 1. expensive as shit, and 2. visually unappealing.  The idea of the invisible fence is like Mehhh.  We'd have to make sure she had that collar on all the time, and she's a bit of a scaredy cat so she'll likely be too afraid to even go outside.  She could even run right through it and then not be able to get back in.  I know this method works for a lot of people, but I'm just uncertain of it.  If you saw what she looked like when we put a simple vibrating bark control collar on her, then you'd understand why this might not work well for us.  She mopes and will barely even move, her entire spirit is sort of killed instantly - and it doesn't even need to vibrate for this reaction.  Sometimes on the weekends if she sees a walker go by, she'll bark in the house and all I have to do is go get the collar and put it on the coffee table and she will instantly shut up.

So she still barks at kids, and might run away.  What now?