Decide how much squash she should drink in a day. Give her that much spaced out through daytime. Give her water in between.
She strips at your drink? Give her water. That way you aren't refusing her a drink, which would feel very wrong to me!
I'd also suggest that you drink your squash in a mug :)
Or an opaque water bottle ... And lie about what you are drinking

Sounds like you're passing on your own dislike of water, which will cause her problems at nursery and school (not to mention the potential health issues).
By giving her a variety of drinks through the day, and some err, deception about what you are drinking (!), you'll get her into more healthy habits.
Slightly counter intuitively, can you try more variety of drinks in order to get her drinking more healthily?
It gets get away from thinking that the only choices are:
squash = yummy
water = bad...
So, offer diluted fruit juices, milk, toddler friendly smoothies etc., healthier squashes (? High juice content ones? Or those toddler ones?)... even a range of different squash flavours might be helpful.
And 'making' her own juices from fruit, like squeezing an orange (doesn't matter if you only get a few sips in the end, it's the fun of it that counts!). Making ice lollies is good too, with fruit juice, or dilute squash, and bits of real fruit in it, or milk based ones .... all to get her used to different drink tastes.
The other thing that tends to go down well are ice cubes. DS would do anything for an ice cube at that age, when he'd turn up his nose at water.
Maybe you could make a big fuss out of making a 'grown up drink', as a special 'treat'? Water with some ice cubes (we make ice shaped as hearts, so very appealing to small beings!), and a fancy straw? You can add gin to yours surreptitiously 
Adding lumps/slices of fruit goes down well too, to take the edge of the water as well as the look of it. You can either do the single slice type of idea, or add lots of chunks. A jug full of fruity water in the fridge could be made very exciting!
If ice cubes might be a choke risk then you could try crushed ice? You could make healthy slushies for you both?
And then only offer squash at certain times of the day, and make it a routine to offer milk/ water with meals etc. You'll get some tantrums when you change the rules, but if you stick to it the tantrums will go...
They're super clever little things, and from what you've said, I'm pretty sure she knows all she has to do is cry and you'll cave in!