Hey JB,
Sounds like everyone in your situation is needing a little empathy. You needed it from your own parents as a child, and from what you describe, you didn't get it (or get enough of it when it mattered, anyway). It's difficult to explain to others how stinkin' HARD it is to parent empathetically when we haven't had that modeled for us by our own parents.
I know of which I speak: I grew up in a household which offered ZERO empathy. It was something I had to learn on my feet as an adult. Counseling helped (I've been very open about that...it's the reason my life is as good as it is now) and two books really helped for me. The first is "How to Talk So Kids Will Listen...and How to Listen So Kids Will Talk" by Faber and Mazlish. This book will give you tried and true techniques for being able to effectively listen and reflect back to your daughter her concerns as well as your reassurances. The second is a book I often recommend for its great disciplinary techniques and its understanding of the child's needs: "Taking Charge: Caring Discipline that works at home and at school" by Joanne Nordling. This book is unique in that there is a section devoted to understanding a child's inner reality of a given situation *while* we discipline. (I think of this in reference to the struggle around naps.) I wouldn't recommend these books just because I like them; instead, I've recommended them to other parents who have found them very helpful in relating to their children and feel more confident now that they are meeting their child's needs AND getting better results in regard to behavior.
On the more personal side of things: I understand your awareness that we don't want to shut down our kids just because we are uncomfortable with upsetting subject matter. I'm not as quick at turning down the radio newsbreaks as I'd like, and sometimes my son hears the harder truths about world affairs. He will ask "did someone die? why?" and we try to use simple language like "bad guys, good guys" and "it's really sad". The other day we were gently trying to change the subject because it had been exhausted and he asked if we didn't "want to talk about it because it's sad, right?" Observant little guy.
The sorry part is a bit harder. Many families often teach that "sorry" is the appropriate end of any conflict which includes hurt feelings. Thus, it's natural that the child comes to expect it of adults who are disappointing them. If you consider that she is needing to hear the word, it's easy to put it into a statement without outright apologizing for the unpleasant (to her) direction you are giving. "I'm sorry you are sad about naptime. We still need to rest. (and here, I'd offer a choice if you can, even a small one like 'which blanket would you like' or 'is there a special story you'd like for our snuggle time' )" or "Yes, I know you don't like to go in the car on errands. You want to know what? I don't think they're all that fun either. I'm sorry that we have to do this now, and I wonder, which toys would you like to bring so you have some fun in the car? (then offer a choice)" For me, this is a 1-2-3: relating, apology (if reasonable) and then the choice. The choice is what helps kids actually move past the moment.
Sometimes we can also transition topics (as you described, not letting an unpleasant subject go), and my husband and I do this with little guy from time to time. "You know, we've been talking about this (sad thing) for a while. I think we're all pretty sad and I'm ready to talk about something new. Here are two ideas: unicorns or teddy bears?" A choice is offered and encourage a flight of fancy... here, you can ask an open-ended question too. "If you had a zoo, which sort of animals would you choose?" or "If you could go to the grocery store and get anything you like, what would it be? What would you put in your basket?"
There are also some good articles online about helping children develop resilience, and I think parts of your question above would be well-met by those sorts of articles.
Also remember (and it's so hard, because I've been here too) to keep finding things to like about yourself, to keep noticing when you make great decisions as a parent--write down those good ones in a journal, as well as those you are wanting to work on and ideas for next time. Give yourself a break and *know* that your daughter is lucky because of your awareness around your own desire to do better for yourself and for her. Changing our habits, our self perceptions-- this isn't easy or overnight work. It takes a lot of time. I've had lots of counseling, am a totally different person than I was 10, 12 years ago, and there are still days that I struggle to deal with negative self-perceptions and other 'hangovers' from my childhood. The fact that you are actively working to break the cycle is really, really good news for your family. Keep on working on yourself, keep on being open and asking questions and give yourself a lot of love, even when it feels really strange to do so. :) We all have inherent worth within, even if we were told we didn't, that we were disappointments to our parents or didn't live up to their own expectations. If you are actively trying to learn how to be a better mom, how to be empathetic and supportive to your daughter, it won't be so hard or take so long for her.
Happy New Year and good luck. Please PM me if you want any details/clarification on what I've described or have any questions.( I'm off Mamapedia after today, in order to get some stuff done in my real life!:))