Getting rid of muddy/ginger looking lowlights in blonde hair.

Hello everyone,
I am new here so I hope that I am posting this in the correct place (and I apologise in advance if this has been answered elsewhere).  I have been reading through these boards all day and it looks like there are lots of knowledgeable people here - I hope that someone can help me.

My problem seems a bit tame compared to lots of posts here - I don´t have a crazy colour and I´ve never done anything to it myself - I always go to a salon, but I currently have a colour that I can´t even bear to look at in the mirror!!

My natural hair colour is that ´dirty dishwater´ blonde that lots of us have.  For years and years, I have had my hair highlighed (I´m not sure what with - the phrase ´hi-lift´ sort of sounds familiar, but it always comes out white, and I keep it clean looking with purple shampoos, silver toners, etc.) The overall look was a very white blonde at the bottom, and a more highlighted look at the roots/midlengths.

For some reason, I decided that I wanted my hair to look more natural, and so last year, I had some lowlights put in a couple of times.  There were supposed to mimic my natural colour, but both times they came out waaaaaaaaaay darker  🙁  After lots of washing with Head & Shoulders, Vitamin C treatments and bicarbonate of soda, I managed to fade them a little.  However, on both occasions, the lowlights faded to a gingery orange colour that just doesn´t shift, and is completely resistant to any sort of toning.  I think that it might be because I have been in the sun quite a lot - perhaps that alters the shade of hair dye?
To cut a long story short, my once white hair is now looking really dull and dirty and orangey and yellowy - just a bunch of shades that I don´t like. 

I have a hair appointment next week, but I don´t really know what to ask for to get it back to its former white state.  I have never had bleach used on my hair before and I don´t really want to go down that road...but I am not sure that a hi-lift (I don´t even know what that is?!) will be strong enough to get rid of these lowlights.  I had thought about using the Scott Cornwall Decolour remover but I am terrified of doing anything to my hair myself! Would I get a better result at a salon if I tried to remove the colour myself beforehand, or should I just leave it all in their hands? My hair is almost waist length and is (or was) my pride and joy, so I am really nervous and very keen to not doing anything further to compromise its condition.  It has been around three months since the last lowlights were put in, and during that time I have ket my hair in good condition and never touched it with heat.

I had my lowlights done in a different salon from my regular one (as I was abroad) so that´s why I am a bit concerned about figuring out what to ask for!  I have also read so many things about how it is impossible to lift colour with colour, and that if you put light colour on top of dark colour then your hair will fall off, and just all sorts of horror stories - I am starting to wonder if I should just leave it altogether and let it grow out.  I am really confused!

I was going to attach some pictures here, but I can´t figure out how to do it. However, if anyone can give me some advice on what I can do to get rid of my orangey lowlights then I would be eternally grateful.

Thank you so much.