Hello!
First, congrats on your new baby! I bet this is a very hectic time for your whole family.
Now to get to your question. Your dog doing what it is doing (Marking, defecating, etc) is indeed because of dominance issues. And this is not good. This is a dangerous situation and needs immediate attention. As others have said, your dog is seeing ITSELF as "Boss over your baby" and that is simply NOT the way it should be. (Your dog should be on the lowest rung of teh family totem pole) dogs are NOT babysitters, nor to ever,ever be trusted with small children. (I am not meaning to sound like I am coming down on you, but only trying to relay the important gravity of this situation)
You need to contact your vet and see about a trainer or canine behaviorist who SPECIALIZES in Large Dog dominance.
In the meantime, keep your dog crated any time you cannot be supervising it directly or interacting with it. Do not allow it loose in the house, and NEVER allow it in the childs room. If you leave the house. Crate the dog. I will post some other links to things you can do as well (In home training and programs)
Warmly,
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Jackie & Max
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