Humans are a totally separate species than dogs. Once the dog learns the heirarchy they'll become accustomed to the different discipline methods. When my niece was born my sister was living at home so we had 2 dogs at the time. Both dogs knew words like "get out of the way" but not in a shouty or aggressive way and Coco liked to lick Chloe's chin (dried milk and drool) but could be called off in a second.
I know Spezza came later than Aly but it could be a bit of jealousy. Coco was always a little jealous of the attention Chloe received, when she got big enough to play with him they formed a better relationship. As for peeing in the house, as Sasami mentioned it could be training (I know this is no longer an issue for you). As dogs get older they have less control over their bladder. Coco used to do his very best trying to hold it in, but going downstairs he would dribble (thank goodness the home owner was replacing the carpets anyway and said it wasn't a problem). I never yelled at Coco for peeing on the floor, or vomiting, or even somehow moving the 100lb kennel and getting on the bed to poop while we were out.
Letting the dog know you understand him and can trust you in times of accidents is crucial.
As for human babies, when she starts to walk and crawl the dog should know boundaries but also know it's okay to go help her and sniff her. Babies who grow up with animals turn into the best kids
!!! (ex: Chloe was scratched by my demon cat over the holidays and after crying briefly she and my mom talked about why he "didn't mean it" and she went right back to playing with him.. Now she's asking Lisa for a "puff ball kitten"!!)
Hm, The cat we had when Chloe was born was a supremely calm and tolerant tom cat. When he was indoors laying down, he was a really good tool for Chloe when she was learning to sit up.. He let her pull herself up on his fur, in fact he purred while she did this!
Illusion the cat came later but Coco was trained by then to keep Illusion out of trouble before he became a problem with Chloe. So I have no offerings there for bad behaviors and discipline .
If we decide to have kids I should hope and pray that Oliver is calmed down, he is curently not a child friendly cat!