It sounds like you are giving up on her and giving her a diaper when all else fails. She has conditioned you to give up and instead give her what she wants. Which in this case, is a diaper to pee in. A child can hold it for a long time, but eventually the urge to go will get so strong that she'll have to go and since she knows she can hold it until nap time when she'll get a diaper, I'd say she has you trained well. Don't despair, you can remedy this.
First of all, you need to stop using the diapers. Your ped means well by asking you to hold off for 4 more months but I have a friend whose child was still wearing a diaper at 5 because he refused to use the toilet. I'm sorry, but that is ridiculous! We don't start teaching our child to talk until they are ready to talk. No, we begin communicating with them from birth. They learn by hearing so we talk to them all the time and encourage them to make sounds all along. Same concept with potty training. There comes a time when a child is just too old to be wearing diapers and I'm sorry, but your child is too old. I can see if night time training is in effect and then you would need a pull up but your child is relying on a diaper to do her daily pottying as well and she is too old.
Do you work? If not, then let her run around the house all day long with no diaper, no pants, no shorts, no underwear. Just totally bottomless. Trust me, a 3 year old is not going to want to pee on the floor or worse, on herself. Also, the sensation to pee will be much stronger without any pants on so she will be very aware of the sensation to urinate. You show her the toilet and tell her that when she feels pee-pee in her tummy, the toilet is where we go potty. It will be up to you to train her and you must be committed to this or it will not work. First thing in the morning, off with the diaper and put her on the toilet. If she doesn't do anything, let her run around the house with no pants on but every 30 minutes or every hour (set a clock if you have to remind yourself...and setting a clock so she can hear it go off is also helpful for her to know that it's time to do something) put her on the toilet. If she still doesn't do anything, then wait another hour. Eventually she WILL pee in the toilet. When nap time rolls around, refuse a diaper. Tell her she cannot take a nap until she pees in the toilet. You are not torturing her as I have taught my 3 children this way and my first two children were totally potty trained by age 2 and my third was totally potty trained by 2 1/2 years of age. This method does work!
Also, you need a reward system for her when she does finally go. It should be a reward (not a bribe) that is ONLY given to her when she pees or poops in the toilet. If you give this reward to her at any other time, you are then defeating the purpose of the reward system. I used Gerber gummy treats. They are sold in the baby section of most stores and they come in little snack bags in one box. I would open one bag and give my child only ONE treat, not the whole bag and the treat/reward is ONLY given if pee or poop was produced. Sorry, but no reward just for sitting there. She must do something on the toilet. Finally at the end of the day at bath time, put her on the toilet and do not put her in the tub until she does something. Now, you may be thinking you don't have time to be sitting with her in the bathroom until she produces. You don't have to! I utilized my time very well. I would put my child on the toilet and say, "Mommy has to go get something, you sit here and go potty and I'll be right back." Often times my child would call for "Mommy" and I'd call right back, "I'm coming, be right there...you go potty and mommy will be right back." I got laundry started, beds made, dishes washed all the while my child was sitting on the toilet! Hopefully, by the time you get back to her, she will have done something. Sometimes they like to do their business in private anyway but when you see she has done something, make a huge deal about it. Clap, and hug her and tell her how happy she made you by going potty in the toilet and then offer her the reward for a job well done. Do not go back to diapers. If she is not staying dry during the night, use pull-ups but the diaper for your child is her crutch and you need to remove the crutch. Good luck and above everything else, be patient but persistent. If at any time you give in, your have lost the battle to a 3 year old and potty training needs to be underway by now.
Another thing is to watch your daughter carefully when she doesn't have pants on. Watch for the pee-pee or poopy dance. It's really not hard to miss. They start wiggling and giggling when the urge is present and that is your golden opportunity to whisk her off to the toilet and let her know that you know that she has pee-pee or poopy in her tummy that wants to come out and put her promptly on the toilet and make her sit there until she makes something come out. She will only be able to sit for so long with that strong urge before something drips out and that will be you cue to start encouraging her enthusiastically!