We have a new 3 week old baby boy and 2 male staffies. When i was in hospital, my hubby took home one of the blankets our son had been wrapped in and let the dogs sniff it and sleep on it. One of then was very protective of the blanket, the other one didn't really fuss at all. 3 days later when we came home, they already had the sent of the baby and they were both sniffing him when we got out of the car. They are both very gentle around him and they sit and watch over him while he is in his bouncey rocker.
I would suggest going the same with your Mum's gs. Take over an item of clothing and let him sniff it and sleep with it for a few days. Then introduce them after that. Remember though. NEVER leave any dog unsupervised with your baby. Its just not worth the risk, even a chihuahua can't be trusted with a baby alone.