You don’t need to take a newborn to the park, OP. She needs your support and responsiveness to make the transition from womb to the world (as above - Google fourth trimester) - and for her that means she needs (needs - not wants, just like she needs feeding and nappy changes) to be held to know she’s safe enough to sleep as much as she needs. Some people have babies they can put down. You don’t, but it’s still very much within the spectrum of perfectly normal newborn baby behaviour. She’s waking up more to the world now and feeling less secure. That’s why she needs more support now than in her first month.
You cannot currently get her sleeping adequately any other way and she may well need that for some time to come, not because you’re creating those behaviours, or failing her in some way, or making ‘wrong decisions’ but because that is her own biological need. The skill to sleep independently is developmental and, just like walking, different babies acquire it at very different ages. You wouldn’t perceive a baby not walking at nine months old as ‘a problem’ - they’re just not developmentally there yet. Don’t see a baby who can’t sleep independently as a newborn as ‘a problem’.
Why can’t you keep her on you while you’re visiting family? As far as she is concerned, she is simply an extension of you at this stage and fighting that is distressing to her. I used to tell visitors or family it was nap time and either cover up or decamp to another room. No, it’s not the pre-baby fantasy of your gurgling newborn being happily passed between all the members of your family, but as I said upthread, this is just the beginning of parenthood being absolutely nothing like you expected!
Trying the dummy as you already have is worth persisting with. You could swaddle her before a pre-nap feed, then when you try a cot transfer, lie her down very slowly starting with her feet and ending with her head to avoid a startle reflex which could wake her. Sometimes doing this into a side-lie, holding her there for about five minutes then easing her onto her back works.
But, hand on my heart, accepting what her needs are and meeting them exactly as she’s telling you, while trying to make the best of it yourself with snacks and trash telly (on iPad with earphones if TV disturbs her) will cause you far less angst/guilt/stress in the long term. Yes it’s boring, but it’s not forever.