I keep pretending I don't know how to fix things so my brother will come over

I'm 34. My brother is 39, married, two kids, lives about 25 minutes away. About a year ago I moved back to our hometown after a breakup. Most of my old friends have moved away, and making new ones in your 30s is harder than I expected. My brother and I have always gotten along, but we're not really the type to call each other just to chat. Growing up, we'd spend weekends helping our dad fix stuff around the house. We could talk for hours while doing something, but sitting across from each other having an actual conversation? Somehow that feels weird. A few months after I moved back, my kitchen faucet started leaking. I knew how to fix it. I'd already watched a video and bought the replacement washer. Instead, I called my brother and asked if he could take a look. He showed up on Saturday with his toolbox, fixed it in about fifteen minutes, and ended up staying for three hours. We ordered pizza. Talked about work, his kids, our parents, some stupid stuff we did when we were teenagers. It was the most I'd laughed in months. So I started doing it again. A cabinet door that needed adjusting. A loose towel rail. Setting up a new router. All things I could easily do myself. Sometimes I even look up the solution beforehand so I know it won't turn into a huge project. I don't want him spending his whole day fixing something complicated. I just want an excuse for him to come over. He always complains that I'm hopeless with tools, which is particularly embarrassing because we grew up learning the same things from the same person. Last Sunday he came over to help me put up a shelf. I already had the drill, the wall plugs, everything. I could've done it before breakfast. He brought his younger daughter along. She sat at my kitchen table drawing pictures while we worked. Afterwards we made grilled cheese sandwiches, and she insisted on leaving one of her drawings on my fridge. My brother stayed until nearly five. At one point he said, "You know, you could probably figure half this stuff out yourself if you tried." I said, "Yeah, probably." Which felt pretty shitty because he's right. Here's the actual confession: I'm not helpless. I'm lonely. I want to spend time with my brother, but asking him to drive over just to hang out makes me feel like I'm taking time away from his family. Somehow asking him to fix a cabinet feels more legitimate, even though it takes up the exact same Saturday afternoon. And I know that's ridiculous. I'm making him do chores when I could just tell him I miss spending time together. Yesterday I noticed the bathroom door handle was getting loose. I tightened it myself. Then I stood there for a minute feeling strangely disappointed that I didn't have a reason to call him. I haven't told him any of this. He's a good brother and I think he'd probably understand, but I'm embarrassed that I've turned being bad at home repairs into my entire strategy for maintaining a relationship with him.