My daughter is 21 months and is also a fiesty one - very hot temper! I try to distract her with toys during diaper changes, etc. Sometimes I give her a wipe and tell her to wipe her cheeks, wipe her ears, etc. It is a game she and my son both like. During our morning and night routines I try to attend to her while she is drinking her bottle - the bottle is comforting for her though it is a bit hard to work around.
Something both of my kids have been responding to lately is this: when it is time for a diaper change I get all my supplies ready and sit on the floor. With my arms open wide I call one of them over and make a big fuss about how much I love them. We do hugs, kisses and tickles. Then we change the diaper and do more hugs kisses and tickles. Then it is the other's turn. It takes a little time but is a lot more fun than the tantrums.
If none of my efforts work, I give her hugs to try and calm her. If she doesn't want held and insists on continuing the tantrum I make sure there is nothing in her way and let her try to work it out on her own. Usually in a minute or two she will come to me for comfort. I praise her when she calms down and I also praise her when we have a pleasant experience (no tantrum or drama). We've been working on this for almost a year and it is getting much better but it has been a slow process. (My son also went through a similar phase that lasted just over one year.)
My daughter also bites when she is mad - she has given her brother a few good welts and bruises. When she goes to bite I put my hand under her lower jaw and tap her lips or cheek with my thumb and tell her she isn't allowed to bite. I don't do this forcefully and I do it to try to help her make a better connection about which behavior I am reprimanding her for (the biting usually goes hand-in-hand with fighting over a toy, screaming, etc).
Good luck to you. Try to be patient. Turn these "chores" into games. Offer a lot of praise for good behavior and be consistent about it.