What is the best time to cruise for 1) a family that is constrained by the school schedule (really, truly constrained—we can’t take them out). They have spring break tied into Easter, so usually in April sometime, summer mid June - late Aug, typical Xmas - New Years. I can’t handle heat very well but want to do one of the Bahamas cruises. I worry about the holiday crowds if we did Dec.
2) me by myself, when I can go pretty much anytime except the major holidays b/c I’d need to be with the family then. I’m thinking either Sept - Oct (I know about hurricane season) or Jan - Feb. Wanting it to be cheapest and least people if I go by myself. Thank you for any insight! All the comments from this forum have been really helpful so far. 
I’d go the last possible week of summer break or first available if you really can not take them out of school.
Alone? Early November or late January were decent for Caribbean. Maybe too cold for Bahamas…?