If my nieces are immunized can they spread measles to my baby?

No. This just doesn't happen. I'm sorry that somebody deceived you.
NO. No, there has been zero documented cases of spread of any vaccine virus strains from the MMR shot to another person. Measles and mumps have zero risk of this. For rubella, there is documentation showing some vaccine virus shedding in the nose and oropharynx of vaccinated people, but still zero cases documented to show that that infects other people. This should not be any risk to your kids.