Nelly, honestly - you should be making the decisions on what/how to feed your baby, not his daymom. She must go with whatever you feel is best for him. She can obviously give advise based on what she sees during the day with him, but ultimately, you get to make the decisions.
My baby is formula fed, but that's because I made the decision to formula feed. If you want to breastfeed, don't stop because his daymom feels he is not getting enough milk. The theory that breastmilk is "not enough" for babies is really not true. If yur paed is happy with his growth, then there is nothing to be concerned about. If your boy is a bit more hungry, maybe increase his solids. If he has been getting 1 tablesppon of solids twice a day since he was 4 months, then I would definitely say it is time to increase that. He could be hungry, but not because your breastmilk is not enough, but it could rather be because he is ready to increase his solid food intake. Perhaps introduce lunch now as well.
Good luck.