your situation sounds exactly like my daughter's when she was 2.5 months old. she was just taking short naps all over the place and i was just so exhausted. i decided at that time to put her on a routine. i don't call it a "schedule" only because scheduling sounds more strict and the idea of a routine is more flexible. as long as it's +/- 1 hour or so. what i did was put my daughter on a routine so that when she woke up, let's say at 7am, 2 hours after playing, etc. she got tired. she would then take a nap for 2 hours. then another 3.5 to 4 hours or so later, she would take her mid-afternoon nap. so her naps would be from 9am-11am and 2:00-3:00/3:30pm. i made up this routine based on the various books i had read, and i found that they all recommended the morning and mid-afternoon naps that you are suggesting. you just need to make sure the morning nap is not too late, meaning that it ends no later than 11:30, and the mid-afternoon nap doesn't start too late, no later than 2pm. then around 5pm, your baby will be tired and will take another 30-45 minute nap. and eventually by around 6 months, she'll be able to cut out the 5pm nap and only be left with the 2 long naps. i think the key is that the babies need to be tired enough to go to sleep, and they usually are after 2 hours of tummy time or active play after they wake up. after you get the routine started, she'll fall asleep almost like clockwork, but of course, plus or minus an hour or so depending on what time she woke up assuming that she doesn't wake up at exactly the same time every day.
i don't know if i'm answering your question....but what i'm trying to say is a routine will help, so she gets tired after play time and wants to sleep.
please PM me if you want more info and perhaps we can chat. i was in your situation and i just got too tired and couldn't get anything done. and now, i'm happy to say that my daughter is thriving on her routine and is 6 months old on monday!