Because time out is so short for our age group it serves the purpose of getting adult attention. She does something - bet it is minorish and not a major infraction - then you interact directly one on one with her, she sits for a bit and then you come back and interact one on one with her again when her sitting is over. Kids will go to great lengths for attention even if it is negative.

Just with anything if it isn't working then time to have a new plan.

Rather than pushing the sharing, playing together I would be inclined to separate them and encourage more parallel play instead. If each has their own things there is no reason for mine. This sounds partly like a maturity thing and partly like a cause she knows it works thing. Let her have her moments and who cares if she gets upset. She needs to learn that life is just like that sometimes. Again take yourself out of the picture.