daytime naps

Louise
My daughter will be 16 weeks on Friday and currently finding it difficult to get her to nap for long... I try and make her nap around 1.5-2hrs after waking, she usually gives signs such as fussing, yawning etc. Currently she's good at being able to go to sleep herself at night (although I'm well aware there's a regression coming..) 
In the day I have to rock her to sleep usually and after she finally drifts off she's wide awake after only 30 mins. Occasionally rocking her some more will make her go back to sleep but often it doesn't... she sometimes has major screaming meltdowns... yesterday's one was at 5:30 after failing to try and get her to nap for over half an hr. I had to take her out in the car to get her to sleep. 
Has anyone got any suggestions... and am
I correct in my theory that proper meltdowns *can* be as a result of being overtired..?