Need some advice

I've been trying to get my hair a pale blue for about a year now. I've had my hair dyed before at at the start of this debacle it was a mix of box blonde, my natural dark-ish brown and a lighter brown done at the salon.

My boyfriend's mom agreed to help me out as she's taken a hairdressing course, but wasn't okay with dyeing my whole head so offered to colour my fringe and two streaks down the back. So we gave it a go, she gave my hair two bleaches at 9% and 12% (I think) and it went a yellowy colour. She said that my hair wouldn't go any lighter and eventually gave up (though this could be because she and her didn't exactly get on during that time) and put on the Crazy Colour Bubblegum Blue. It was.. alright, a turquoise-bluey colour and I kept that for about two months as it faded to green and no amounts of reapplication of the dye would make it even slightly blue again.

My mom recommends a hairdresser (she was against having it done out of a salon to begin with.) I go to them, they suggest I have a dip dye and fringe in blue and I'm worried about having to do my roots regularly, so I agree, having shown her the light blue I want. When she finishes, my hair is an, albeit beautiful, dark blue, in varying shades which she assures me is the most permanent on the market and will take months to wash out (this isn't even the colour I asked for.) After three washes and a stupid mistake involving a swimming pool it's basically green, I go back, have the dye reapplied and it goes green again after a few washes and that's where I am now. I notice when she puts the dark blue on, the streaks that were dyed from the previous time are the lightest and tend to stay blue longest, for obvious reasons. So I figure it's going green because the blue fades to the poorly bleached brown and looks green, except in the bits that were bleached more.

I've figured at this point, nobody is going to help me but myself, and I know that it needs to be bleached further. It's been about a month since the hairdresser bleached it (though it must have been a particularly weak bleach) and I've got a Jerom Russel Bblonde maximum lift blonding kit, which I intend to use over the green and then put some Bubblegum Blue over that. I've never bleached my hair myself before (had my sister do it last time I used a box blonde)

Basically I'm asking, am I going about this the right way, is there anything I should know, how should I go about this?

Thanks :3