I didn't think I would be able to groom my dog either. Prince is 7 months and stays in mid-air most of the time - he's part Poodle so he likes to jump.
I don't bathe and groom the same day, that way he won't have to be still for too long. When I groom, I have everything laid out beforehand. I put him on top of the bathroom vanity and tie his leash to the towel rack so he can't fall off. I clip a little with the clippers, give him a treat, clip some more, give another treat.
We have been practicing the "Wait" command at home. "Wait" means freeze, "Good Boy" means unfreeze. This give me just enough time to do most of the face area. Maybe when your baby is a little older it will be easier.
Prince has black nails and I am scarred I would cut too much so I take him to the vet for a mani/pedi.