One trick I use with my 3.5M DD for the first awake time of the day is: After feeding her, letting her have some sit up time, and play time (usually she starts yawning by 30min up, and she would be quite happy to go back to bed after 1hr including feeding time) I lie her down on a folded towel in the bathroom while I take a shower, get dressed, brush my teeth etc. The sound of the shower keeps her pretty calm, I leave the lights off so she isn't staring right at them, and I talk to her if she starts making her tired whining noises. It takes me about 15 minutes, but which time she is quite tired. I put her to bed, and it takes her about 10 minutes to go to sleep, so that puts her right on track for being up 1.5 hrs.
With regards to the short naps, there is a lot of good info in the 45 min nap discussion area.