Can a child be infected from rubella virus even he is vaccinated?

Unlikely: Vaccines aren't perfect but the chance of this is quite low. Best wishes!

Yes: Protection from the first dose is expected in about 85% of the population, this rises to in excess of 95% after a second dose given at least a month later. The current routine in the US includes doses at a year and 4-5 yrs which integrates vaccinations with day care/school entry. Recent measles outbreaks in the US were noted from imported cases in mostly unvaccinated but some once vaccinated kids