Assuming FCP is Final Cut Pro I’d just buy a new(er) MacBook, or maybe look at the iPad version. FWIW I’m the same, I’m software/ecosystem-locked to Logic Pro, I don’t use it much at all, but I’d not want to not have it. It is one reason I have a MBP rather than a cheaper Linux laptop.
Another option might be a Mini connected to the TV assuming you have a decent one in the room. I figured out with the right screen resolution I could use a computer connected to my 50” 4K TV from the sofa easy enough, but it just doesn’t fit with my workflow at all (as stated I use an iPad almost all of the time).
I doubt that you’ll find anything more suited to your needs than a newer MacBook of some description. Using a Mini and a less good laptop, netbook or whatever for remote access just sounds like hassle and frustration to me. The only other contender is an iPad, which has a version of FCP (subscription I think), but that form factor may not suit your requirements anywhere near as well as it does mine.
PS I noticed the iPad version of Logic is on a subscription, so they can keep that. I’m not paying a monthly fee for something I’ve already paid for!