Same here,
Husband is happy to cuddle or play when he's in the mood, but the dogs are MY responsibility, always have been. He seems to be a clone of Brainless' husband! Happy to help with births, but not the sleepless nights or cleaning up after pups, drove me to Ch shows and helped me with heavy stuff, but drew the line at open shows, I had to fend for myself there. He does love them, just doesn't want the work, and that's fair enough, it's the agreement we made.
Had my first pup when DS was 2 and DD 16 and I fully expected it to be like having another baby but on speed - they are more mobile and much quicker from an earlier age ;-) Good job as first pup was a lunatic and
very bolshy!
I also did ALL the training, and had to train my children and husband at the same time. Pup was easier to train than the others :-(
Dungonnell, have you considered that your little one's incontinence may be due to urine infection and the timing just co-incidental? Just a thought.
Re your older child playing up/getting into 'fixes', I would say that has always been my experience, even when just using the phone, suddenly they either need me NOW! or when little, would instantly get into mischief! I thought that was normal?

However, you clearly feel you can't cope and that may be because you aren't feeling well at the moment, or maybe just underestimated what having a puppy would be like.
Whatever the reason, you are putting the pup first. Many people wouldn't do that, and for that you should be commended. It's a tough and heart-breaking decision.
Give yourself a break. Maybe, when your health issues are sorted, and the children older, you will be better placed to have a dog.