We have the DSC every weekend, though not in the week. It is hard to get any quality time with my own DCs, (13 and 9) and I also like to try and give them a bit of one to one time, which I think is good for all kids, even if they aren't living in a blended family. Sometimes I take one or both of mine out on shopping trips to buy clothes or shoes (and then also take in a café or something). But that might not work so well for you if you're also the person who buys the DSC clothes.
I think your idea of doing the driving with your DS over to his dad's is a good one. Let him sit in the front of the car and you'll have a bit of a chance for a catch up even just driving there. If it's too cold for the park, you could always buy him a hot chocolate or something in a café. That's one of my DS's favourite treats.
But you're right, you'd find it much easier to spend quality time with him if your DP did the same with the DSC. How many of them are there? If there's more than one, you could suggest he does some one to one too with one of them whilst you look after other(s) at home, so that doing things in different configurations becomes a bit more the norm? I sometimes shut myself in DS's room to look at his school work and homework, which gives him a bit of one to one time. But guess if yours are there 24-7 then the DSC would be just as in need of this from either you or their dad.
I'm also planning a few days away this summer with just my two - doing outdoorsy things that DSC are not so into. I do think it's OK to do that. Doesn't mean I don't want to live in the extended household the rest of the time. Thankfully DP understands this.