Travelling with family members, whether cruise or other type of vacation, will totally depend on the family dynamics, expectations, preferences and how well you all get along in general. Haven't cruised with my dad yet - he won't go on a
DCL cruise because there's no casino - but DH & I did do a four day trip together with my dad in Jamaica. It was for my niece's wedding. She was getting married at the Riu Negril but we knew that it wouldn't be to our tastes so we booked a small boutique resort just a few minutes away. We shared a two-bedroom cottage and spent the entire four days together (we didn't leave the resort except for the wedding). We had a lovely time. I was concerned that the rustic style of the hotel might not be to his taste but he loved it. We just lounged around the resort and bobbed about in the pool but would have done some excursions had we been there longer and we pretty much agreed on what we would have like to see so that would have worked very well.
If we went on a cruise together with my father, whether DCL or another, I think we'd have a good time too. We'd probably split up for some of the time, maybe go on some excursions together and some apart (we'd all like history, sightseeing, nature, but not anything really adventurous and no gourmet dining for dad - we'd do those latter two on our own) and we'd have to figure out what seating time for dinner. We prefer later, he prefers earlier (that's a definite discussion to have upfront before booking as is will you eat separately if you can't agree).
If I cruised or did a vacation with my sister, she'd be happy to do whatever I wanted as long as she didn't have to do the booking but she's very easy going and enjoys just about anything. She spends two weeks with her ex-husband's parents in a timeshare in Barbados every year and they all get along really well. I love spending time with DH's aunt (we stay at her place and sometimes spend the entire day together in the kitchen yakking until the wee hours of the night). DH's cousin stayed with us for 5 weeks and we hated to see her go back home. My brothers-in law on the other hand - I can't see ever going on any kind of vacation with them. All they ever want to do is either sit on the beach (younger brother) or hang out in a bar (older brother). They don't like spending money (everything is a "rip-off"), aren't interested in history, museums, music, meeting other people, or anything we are interested in. That would be a brutal vacation. And I can tolerate his sister for only about 2 hours at a time without wanting to throttle her.
Can you all get along for those number of days? Do you like to do the same things or are you willing to split up to do them? If you are all on the same page it can work very well; not so much if you don't. Of course, the dynamics of a BF versus spouse coming along with family members is different and is dependent on not only how well he gets along with your family but how well they know each other, how long you've been together, whether they view this as a long-term relationship, etc. If it's a relatively new relationship or they don't really know him, it could get awkward when you're in such close proximity and there's no way to get away completely until the cruise is over. First thing to do is talk it over with your parents and see what their initial response is. That will give you your best indication of how, or if, it will work.