I think all of the suggestions for weekend activities sound fun and interesting, I do however think also, that you might be looking for a longer-term advice. Your kids are just of a great age where their childish activity can grow into a meaningful passion, given the correct environment that will allow them to choose and get INTERESTED in any sort of subject (which later can illustrate your weekends with trips to museums or competitions). There is a plethora of things to try out and make a hobby out of it. I suggest for you to do some light research on any desired topics you feel like introducing to your children, and that alone can have the kids excited about learning something new (which according to psychology is asked for by a teenage brain). It is vital to give them support in developing a true understanding, why something is interesting and can become close to them. You can discuss the history of development for pretty much any collectable items, you can explore the variety of sports available for individualists and team player kids, you can visit cool art galleries or music places to expose your children to where expression reaches beyond words (greatly suitable for those with rebelious position that is so common in the teenage years). The exploration of choices alone should give you plenty for the weekends in terms of learning first of all about the pond from which they can choose. Then come the tryouts, the visits, the talks with the Parents, eventually helping the children discover not only new longer-term interests, but also a new angle to the parent figures in their life. I wish you well with that!
