You need a helper column of sort numbers, so keep your groups in order, and the headers in the right place, but to allow sorting based on any other column. Your helper column should always be the first sort range, ascending, and then the other column(s) should be secondary sorts. You also need a slight adjustment to your data set, so that the pitchers list for any team starts one row below the team row
For example, with a new column A, and B filled with what had been in A:
1 Team
2 Reds
3 Reds Pitcher 1
3 Reds Pitcher 2
3 Reds Pitcher 3
3 Reds Pitcher 4
3 Reds Pitcher 5
4 <Fully blank row>
4 <Fully blank row>
5 Nationals
6 Nats Pitcher 1
6 Nats Pitcher 2
6 Nats Pitcher 3
6 Nats Pitcher 4
6 Nats Pitcher 5
7 <Fully blank row>
7 <Fully blank row>
With that layout, the Reds' pitchers will be sorted only among themselves, as will the Nats' pitchers, etc.