If dd decides she doesn't want to go in the pram I explain to dd why she needs to go in (safety, too heavy, need to be quick) and then say I am going to count to three and then put you in (so she knows it's coming). By the time I get to three dd has usually calmed down and goes straight in. I know how impossible it is to put a stiff-as-a-board toddler in a pram, so fingers crossed she understands you need her to do this.

Otherwise, what about a trike thing you push along? It would save you carrying her. Our local toy library hires them out.