Helpfully the below is helpful...I've bolded specific words to help differentiate the advice on particular issues!
Age is your biggest issue as Golden Retrievers really don't mature until they are 3 at the earliest, in my experience. Even then, they'll stay 'babies' (i.e. prone to being a bit manic, excessively mouthy and generally just irritating) until they're 8/9.
For training, I would go back to basics (sit, stay, down, extended stay etc) at home. Reward her for being calm and get 'ahead' of the mouthing. Once she has done as bid, give her the treat straight away - don't wait and give her that chance to jump up. I'd also incorporate it into her walks. Really use the training to tire her out on walks. But use high value treats to do it. Also re-train walk to heel.
I would stop games of tug. It is, as you've guessed, bad for encouraging mouthing and jumping up. The problem is it encourages them to use their teeth/mouth to get what they want. If you're the one playing with her, that'll also contribute to her being more willing to listen to your partner but not to you - as much as I love Goldens, they are a bit thick and will associate one human as the 'fun' one. It's also bad for a developing retrievers joints. If you watch her play tug, she'll be putting all her weight on her front legs - to try and gain leverage to 'yank back' - which isn't ideal given her age.
On exercise, I've often found people think they're giving their retriever adequate exercise, or the right training, but they're very often not - not out of malice, or even not understanding, but because retrievers are just 'built different'. Goldens, in particular, are quite challenging as when they're young they don't necessarily have the stamina to do long walks but need them. That being said, your girl could probably nicely do another 20 minute walk in the evening - just to give her that bit more stimulation.
It sounds to be slightly like she gets 'zoomies' and gets overstimulated which is perfectly normal for her age and breed. You may not want to try it, but I would recommend a giant child's cuddly toy (you can get them off Amazon for about £20/30). Whenever she gets overstimulated at home, or you can't calm her down, but you know she can't take anymore exercise it's worth giving it to her. I have had to do it with my boy (he's turned 3 this week). His 'mania' was so bad when he was younger, and his energy levels so high, that I just couldn't settle him. In the end, giving him a giant cuddly toy and letting him hump it for 10/15 minutes a day did wonders. It is, perhaps, not the nicest and most skillfull way of training a dog (and I know lots of people frown on it - but it's advice I've given before and others have found it helpful). The problem with a young, high-energy, breed that you can't over-exercise due to their joints so there are really very few avenues available to you. Whenever my boy has a manic moment now, he goes and sits in front of the giant stuffie and I know he needs 10/15 minutes to himself in the back garden. Then he comes in and goes to sleep. Sometimes when your dog is manic, the best thing you can do is just to let them go for it.
Don't forget that retrievers were bred to have things in their mouth. It's literally in their nature. Which, unfortunately, makes them terrible thieves but - more importantly - can also make them prone to resource guarding. You're doing everything right in fending off that particular issue. So, when she tries to take things off you, and you tell her to leave it you also need to offer her an alternative - a small toy of her own to carry, or a high value reward. She's not necessarily being disobedient, or not wanting to listen, it's just in her nature. My boy can go an entire walk holding my wrist in his mouth - we're talking 90 minutes of him walking next to me, suckling on my wrist which is beyond disgusting but ultimately it's a form of comfort for him and it's what he was bred to do.
She'll get better as she gets older. Give it another year or so and she'll begin to settle properly - as you say, she's lovely that 98% of the time it's just that 2% where she is, sadly, a Golden Retriever adolescent and therefore a massive twat.
There's a 'Beyond adolescent' thread on the doghouse where a bunch of us whinge about the horrors of owning dogs (lots of gundogs on there). We also talk cake and coffee...but you might find it helpful for hints and tips on working through her issues. There's a few spaniels the same age as your girl!
Sorry that got very long..