Don't sweat the small stuff. And tummy time is VERY small stuff. My first child hated "tummy time", too, and I was starting to get dubious of the whole thing, so when he got upset, I would turn him back over, or pick him up. Now I'm convinced it's a complete waste.
I noticed that if I held him on my shoulder, he would be just fine with lifting his head, and he gradually was able
to support more and more of the weight with more control and less wobbling for longer and longer. When they are on their tummy, they have to hold all the the weight - but if he was on my shoulder, it was easier because he was almost vertical, and didn't have to lift it completely.
Occasionally, my husband would fuss at me because I wasn't rigorously sticking to the mandated "tummy time schedule", and *he* took over tummy time. But it quickly became apparent to him, also, that we had to find a better way.
I found that when I had him in an inward-facing baby carrier or sling, my baby was able to gradually work on supporting his head, and he would do it on his own when he was interested in some sound or wanted to see something. And when he had enough neck strength, I got one of those "Ergo" baby carriers that go on your back so you can actually *do* stuff. (Yes, and I've seen photos of women planting organic gardens with a baby on their chest in a sling, but I had a difficult time just emptying the dishwasher.) But with the baby on the back, I could do *almost* anything in the kitchen. (WARNING: Never try cutting onions with the baby in a back carrier - Mom's eyes start tearing up, baby's eyes tear up, baby starts to wail and pulls mom's hair, mom cuts her finger - all in about 15 seconds.)
So I gradually came to the conclusion that tummy time was a crock. If the kid doesn't mind it, then fine. But if they
are miserable, then it's not worth it, they *will* get plenty of this "exercise" on their own, especially if they spend lots of time more or less vertical. Now, to be fair, maybe babies who are always being moved from carseat to bouncy seat to crib *would* benefit more from tummy time. But I think they would benefit a heckava lot more from being held. It's human touch that builds the dendrites, which is why baby massage is so good for the infant brain.
Needless to say, when my 2nd baby came along, we didn't fight him. We put him on his tummy every now & then but ended it when he let us know he had enough.
Look at it this way, if failing to do tummy time is the worst thing you do as a parent, your child will have a charmed life. The worst POSSIBLE scenario is that it takes her - what? maybe 2 weeks longer to learn how to crawl. Tops. Big deal. That's 2 weeks that you won't have to worry about her crawling over to an electrical socket or over to a bug she wants to put into her mouth. It's not worth the stress for either of you, in my humble opinion.