Jason,

If I understand correctly, you want each team to play each team in the other division twice. There are 7 teams in the other division, so that needs 14 weeks. The best you can do in 13 weeks is play 6 teams twice and 1 team once.

Suppose the divisions are $A$ and $B.$ In week 1, $A_1$ plays $B_1, A_2$ plays $B_2, …, A_7$ plays $B_7.$ In week 2, $A_1$ plays $B_2, A_2$ plays $B_3, …, A_6$ plays $B_7$ and $A_7$ plays $B_1.$ Just continue the pattern and keep going. when team $A_i$ plays team $B_j$ in some week, they play team $B_{j+1}$ in the next week. If $j$ is 7, then “wrap around” and take $j+1$ to be 1 (note $A_7$ plays $B_7$ in week 1, and $B_1$ in week 2).

Hope this helps.
—Victoria

PS If they play each team in their own division twice, then 12 weeks are needed. Each team can play every other team once over 13 weeks.