Child tantrums whenever invited to go in the buggy.
Tantrums when told to walk instead.
Why doesn't she want to go in the pushchair or walk herself? can she tell you, out of the moment? Or can you work it out from her actions?
If she wants carrying, how about a rucksack or sling? http://www.thecarryingkind.com/products/shw-detail.asp?pid=168
If she wants a snuggle, why not sit on a bench together for 20 minutes with a drink and a snack and a favourite book or a sticker book?
If she isn't ready to leave the place yet, why not keep playing till she's finished? It might take a while to overcome a past history of expecting mum to make her leave before she's ready - the first time it might take ALL DAY playing around the park entrance, but in time you'll find that if you allow plenty of time and don't pressure child to leave, she'll leave when she's had enough and wants to go and do something else. Make sure you take fun things to do yourself, like a book or magazine, and plenty of snacks, in case the park is an all day activity
If she wants to walk s-l-o-w-l-y, can you walk at her pace and enjoy every snail and pebble and leaf you pass?