I don't think that tying her into her bed at naptime is a good idea at all for a variety of reasons. Seems to me that having her restrained like that could lead to some serious emotional issues and possibly more behavior problems as she attempts to rebel against this unwanted restraint. Also the lack of control and feelings of powerlessness at being restrained could lead to emotional issues as well.
If she is willfully holding it until she gets to her naptime bed then you already have a power issue going on.
What would she do if naptime were somewhere else instead of alone in her room? Seems that the quiet and private time is an opportunity for her to make a mess, how about removing that opportunity entirely?
You don't say how old she is nor long you've been attempting to train her, so its difficult to assess. Also I don't know if she'll use the potty for urination and only withholds bowel movements.
But first I'd move naptime so somewhere where you can supervise her and as soon as you catch her undressing (which is usually after a bowel movement I'd bet), then I'd pick her up and say, "Uh-oh, you didn't get to the potty. Now let's clean-up." and have her help you clean-up. Possibly a question of, "Do you think you might go some more?" and ask her if she'd like to sit on the pot.
Maybe even schedule something to happen after naptime that she really likes, like to sitdown for a special treat or an activity. No doing the activity or the treat unless she poops in the pot. Even refer to this throughout the day to remind her. If this behavior is something she can control, she'll more than likely decide to control it for the reward. But you must help her along if its not all about control by monitoring closely her activity.
If moving her naptime space doesn't seem possibly then possibly a baby monitor with a screen (CCTV) you can pick these up cheap at places like Sams Club or on Ebay (some will work through your computer). Then again, try to see if you can catch any behavior that indicates she's about to go, is going or has gone and catch her before she has a chance to make another work of poop art.
****Apparently I misread what was written and thought that the writer, J. meant "tying" in bed when the writing says "trying".
My apologies to J. and her family as I certainly don't think for a minute that she's abusive or anyone else is. Actually, I didn't when I wrote that either, I wasn't making judgment then and certainly am sorry for the error.
Again, my error in misreading her request. I guess someone should tie me up and keep my hands from typing before reading these things completely!