Can I run two 15amp breakers (in a 70amp panel in my shed) off of a 20amp breaker from the main 100amp panel?
Since the feed from your main panel is on a 20 amp breaker and 20 amps is allowable for lighting and 120V outlet circuits, there's no reason to add a subpanel. The 20A breakers you'd put in the subpanel would be redundant. If you want a master switch in the shed, I'd suggest using a non-fused SPA/air-conditioning disconnect box. These are typically designed for two-leg 240V but you can just use one side.

All of the above assumes that you are in the USA and are keeping the circuit 120V and not 240V.