Elizabeth has always hated lying on her back to the point that we did diaper changes upside-down on her tummy. The last round of swimming lessons wanted her to float on her back every lesson, which usually took every trick in my arsenal to accomplish (ie: M&Ms are magic). Even so, she'd often panic and try to sit up instead of relaxing on the water. A thin floating mat available at the pool was helpful but it was clear we still needed to work on this skill.
Turns out she also hates water being poured over her head at bathtime, so we negotiated a deal. She'd learn to rinse her own hair in her own time by lying down in the "water bed" tub, and I'd quit dumping buckets over her head. Now we just have to work on the floating part...