Wanted to say that if you need a sleep though the day, let her sleep ON you!! I found that in those early days, dd would easily sleep on my breast, right inbetween my boobs Don't know how heavy your bubba is, but it might be worth a try.
Lay down in the middle of the bed and just put some pillows under your arms and lay like Count Dracula while dd is sleeping on you. It might be a tad to get used to, but I could doze for about 30 minutes like that. It's worth a shot!!

PS - Your not a bad mommy, just tired and unsure. Sounds a lot like I was when dd was that small!!!