I travel as a single parent all the time. My son says Disney cruises are the best the best vacations ever because we each do our own things that make us happy and then just come together for meals. I'm a loner and an introvert so being alone doesn't bother me at all. That said, any time I've wanted to join something (trivia for example), I've always found a team to welcome me with open arms. We sit every morning at breakfast and kind of plan out of day, see if there's any events we want to do together or any must do's either of us want to do separately.
2 of my 4 cruises I've been on, I've been placed with other single "parent" travelers at dinner (twice it's been grandparents/grandkids). I've not made life long connections like some people, but it's been perfectly pleasant.
If you've not joined a cruise meet up group you might want to do that. Another single mom on my last cruise kind of got adopted into a couple of families so she had more people to spend time with (like I said, not really my thing so I didn't look into it).
For the older kid, you may want to make sure he goes to Vibe the first night as the older kids seem to make connections that first night (my son is 11 and didn't mind not having "friends" through the whole cruise - he was happy just hanging out with whoever was in the club at the time, but that's the kind of kid he is).
Have fun!