Your issues with your mum aren't 'clouding' your judgement - they have helped form your judgement.
Your judgement is that whereas for many families, this level of intimacy is good, positive, symbolises love, this isn't the case for you, and your instinct is to be suspicious of your mum's motives. Why? - because you feel that coming from her it signifies intrusiveness, it's inappropriate.
It's up to you to sit back and analyse that and honestly try and work out if your judgement is fair or not.
Because there isn't a right or wrong with stuff like this. If your mum was overbearing, privacy-invading, liked trampling over boundaries with you and you see that starting to happen with the mother-grandma-daughter dynamic, then that really is fair enough. And the answer to that is, keep her at the distance you're comfortable with.
Take this as an object lesson maybe. If you want a certain level of intimacy and no more, then make sure it doesn't happen. Don't leave your DD with her overnight in future. Work out a way to make it work for you and your DD and also your mum, without letting her take more than you're comfortable with.
Now there will be a few people who are lucky enough to have warm, loving, positive and uncomplicated relationships with their mums who would see that as sad - and it is in a way - but as someone who had a very complicated relationship with their mum, created in part by having an utterly awful grandmother who did her best to undermine my mum to me for years and years, I say - if you can honestly say your instincts are just, trust them.