Oh, Lynne, I remember that age ALL too well! It was right around 10-11 mo that Tyler was doing the exact same thing. It drove me nuts. Some days he'd skip the AM nap, some days the PM nap, and I never knew which one. Either way, he'd be ridiculously cranky by the time dinner rolled around. It sucked. I went ahead and cold turkeyed him to 1 nap at 10.5 mo, and it didn't last. He frequently fell asleep during lunch with food in his mouth, and started with the early wakings within a week. That made it pretty easy to go back to 2 naps, but the early wakings took a little longer to go away for good. He finally transitioned to 1 nap for good a couple months later at 13 mo. Between 10-13 mo, his naps were all over the place, and it was ugly. Totally normal.
What we did end up doing was limit his naps big time. I know everyone tries to avoid short naps like the plague, but I just needed to keep him on 2 naps until he could handle longer awake time without getting overtired. I never let his AM nap go beyond 1 hr, and we started treating the PM nap like a catnap and woke him after 30-45 min. Eventually, both of his naps shortened on their own to 30 min each. When he started skipping THOSE, that's when I knew it was time to make the switch to 1 nap. It took a little experimentation to find the right sleep times to get us through it, and we had to adjust often for sleepy days, but it worked. And believe it or not, when we did cold turkey him to 1 nap at 13 mo, he only had a few rough days of taking 1 pitiful 30 min nap before lengthening it on his own.
Hang in there...that's such a rough nap age, but it will pass!