It's been a while, but we flew Lufthansa Seattle to Frankfurt, and Lufthansa to Ljubljana. I believe currently the only option from Frankfurt to Ljubljana is Lufthansa. I'm not a huge fan of Lufthansa but they (usually) get the job done.
About booking separate itineraries: I would try hard NOT to book two separate tickets. If you are on two tickets, you risk problems if your inbound flight is late (having to buy a new, same-day ticket, which can be shockingly expensive). While it's a short flight and there are rail options, misconnecting would be a big headache, not something I welcome at the beginning of a long trip.
If you really want to buy separate tickets, allow LOTS of time for the connection. I would want at least 4-5 hours.
Personally, I'd try hard to book it on a single ticket. You didn't mention where you are coming from, but Lufthansa is a huge airline and has many huge partners (eg United), and I see no reason to avoid them. I would not say that the integration between United and Lufthansa is "broken" (not in my experience). I fly United quite often and while they're not perfect (what airline is?), I think they're good enough (same goes for Lufthansa).
If I was flying to Ljubljana this summer, I'd probably be on United and/or Lufthansa, and I wouldn't be concerned about it (any more than I'm concerned about flying any major airline) - although I'd be tempted to try going via Istanbul on Turkish Airlines if I could.