My dc all play 1 or 2 instruments which I think is great (and yes, my grade 8 in a totally different instrument helps!). They all do a sporting activity, all go to a uniformed org (scouts/brownies).
I'm not in any way pushy, although I'm on my dd2's back a bit this week to practice for her violin grade 2!
The "pushiest" thing I've ever done is send them to a bilingual school. They love it, it's very relaxed (state school, not private) and they've all become effortlessly bilingual by going here.
Tbh, I'm not convinced Oxbridge is such a goal. There aren't any state grammars in Scotland (purely comp in the state sector and we would never go private) and my dc are already showing skills that we can easily encourage without being "pushy" (we're both high achievers with RG degrees).
Dd1 is very artistic and hopes to attend either Edinburgh college of art or Glasgow school of art (she's only 13 but has researched it herself!) or possibly Central St Martins in London.
Ds is already designing apps for his phone (at 11) and has already decided that he's off to Dundee Uni to do computer science then he's going to work for RockStar games (they did Grand Theft Auto, he's never seen it but a friend did human animation on the games and he's my ds's hero, and has agreed when ds needs school work experience he'll give him a place for a week!).
Dd2 currently wants to be the new David Attenborough. I'm not sure what the degree course for that might be?
I don't push. I encourage, I open up doors for them when an interest develops, I facilitate the things they want to do while providing an all round good experience. Pushiness would put my children off.
Going to a private prep, a super selective grammar wouldn't meet my dc needs. The bilingual education they are getting can't be bought. Oxbridge doesn't feature in my dc's ideas (if it did I'd help, but I'm not pushing that way or any way) and I want them to do what they are best at, what they love the most.
With music, sport etc I've encouraged breadth, which is essential. I'll encourage anything else. But if you have to push, is it really worth it??