First, you sound verey "in touch" with your kids and that is to be commended. It is a big age difference, and you discribed it very well. My kids are only 4 years apart, and that is bringing up challenges too but not quite the same.
I think that you need to emphasize family time with the kids, and frankly, tha tneither be allowed to dominate the situation. I know it is hard iwth a three year old, but you need ot say clearly in front of them both "Don't interrupt your brother" or "Let's watch what he is doing." Let him be the star sometimes. But the same is true in reverse, "Look how well your sister learned to do this and it's her very first time." This kind of language shows appreciation for both kids strengths and shows tha tyou value the unique relationship you have with each. be careful tha tyou are respecting the kids the way you want to be respected - don't let either one of them dominate.
I also think tha tfinding something that they can do together and that the 3 year old can learn from the big one would be great. Like playing game son the Wii, for instance, or board games or card games. Ask your 12 yearold to take the lead to teach the younger - reading, building wiht legos, whatever. And you back off whan tha tis happening. Allowing him to "help" you and see how hard it is but also how fun it can be will making him see the challenges and benefits of the little one.
Ultimately, I think you need ot encourage and find time to be alone with each at least once per week. They don't have to and shouldn't do everything together. Take your son out for a movie with Mom. Take the three year old to the playground by herself. They will learn tha tyou value each of them, and learn patience for being on their own.
Ultimately, the three year old will mature al lot in the next year, and it will get better in some ways. I think, as long as you teach them respect for each others differences, and respect for the job you are oding as a MOM in trying to be there for them both, then you are giving them a good life lesson about family.
As for actual activity suggestions, cooking and baking together is a great activity. You just need to plan seperate roles for them and be prepared to avoid boredom. A 12 year old for isntance can cook on the stove while the 3 year old makes a salad. But you need to do the prep work as much as possible so that they both have something to do and you aren't chasing the 3 year old around. Also, let your three year old watch some movies or color, so the older one can get some conversation and reading time with Mom. And then be tough, and don't let her interrupt! If you bowl or play miniture golf, pay for the little one to have her own turn so that you can compete with your son.
So, all in all, I think it is about the language and values you demonstrate. Teach them to appreciate each other. And it is about planing. They don't have to do the same activities at the same time, but when they do, they need to respect each other. Good luck.
PS - I think I totally screwed up who was older , the boy or the girl. Sorry, hope it still makes some sense!