You were hired to do a certain job, for a certain length of time. You left (for a good reason), leaving the company in a lurch. You need to live with the consequences of your choices, even if this particular choice was forced upon you by personal tragedy.
Understand that the company has a certain time-frame within which work needs to get done. Management may be understanding of your circumstances, but at the end of the day they need someone working to fix the company's problems. It's their responsibility to find someone who will - it's nothing personal.
Also understand that your leaving means that the company will have incurred certain costs: money spent to on-board another intern, bring them up to speed, and then get them to complete the tasks that you should have been assigned.
It's understandable that your manager would feel uncomfortable giving you a letter of recommendation under these circumstances. After all, you weren't with the company all that long, you left them hanging, and you've caused them a headache.
This is not to say that I am berating you for the choice you've made. Family is important, and you had to be there for yours. That's a difficult situation to be in, and you made the choice that made the most sense to you. However, also understand that your employers don't owe you special consideration, even if your circumstances are difficult.
As to how to explain the situation to future employers, simply state the truth: you had to deal with a family emergency, and suffered a personal loss. You needed time off, and your employer obliged by laying you off instead of firing you. It was unfortunate, but - thankfully - not an every-day occurrence.