Mohamed had very poor knowledge of Tora and Bible so there are numerous times in the Koran where he makes mistakes and gets confused about names and such. For example Mohamed claimed that Moses was raised by Egyptian king's wife instead of his daughter. This is why Mohamed had to cover his mistakes by saying the "Jews changed the Bible". However in your case Mohamed was right. Abraham kicked Ishmael and his mother out, not Jacob. But mohamed goes on the say the Ishmael received the "Birthright" when clearly, he did not. That's why he was kicked out, so that their would be no dispute over Isaac receiving the Birthright.
Also, Mohamed's praise for Jesus is in name only. Mohamed did not believe the things that Jesus preached as a matter fact Mohamed preached the exact opposite of Jesus and performed works contrary to Jesus. Jesus did not behead his enemies nor did he enslave their wives. Mohamed preached jihad, while Jesus told his disciples to "shake the dust from your coat and move on when people do not receive your gospel."