Im very sorry for your loss, losing a parent is incredibly hard.
No I don't think you're being unreasonable, but I think you're being unrealistic based on what you've told us. It appears you habitually work long hours, sub in for your flaky manager, without anyone being overly concerned for your welfare... why would you expect them to give a crap now? They haven't exactly demonstrated their strong management and commitment to work-life balance thus far, it's not a massive shock they are lacking any compassion now.
If you are unable to work you have the option to call in sick too. You don't have to step up to cover your manager. You just say No. You do your own work and you email the client, copying Sick Manager and copying the senior management , telling client to talk directly to senior management about covering the gap.
Then you work to rule.
You've let them exploit your goodwill, making the mistake of thinking they will reciprocate. That is unfortunately often the case. The company doesnt care about you, nor does its management. They just want to get as much work done, as cheap as possible. You feel betrayed, quite rightly, you thought you had a good relationship with the company but it turns out it is just transactional after all. They take what they can, they give as little as possible in return.
Sobbing at random times of the day and night is very normal whilst bereaved, I regularly break off work to have a cry (my mum died in October and I had to be back at work the next working day, so I just had the weekend to compose myself). It requires nerves of steel to keep going. After my dad died I was a real mess, but this time with my mum I anticipated how awful it would be, and just kind of willed myself to get through it. Occasionally I look in the mirror and dont recognise the haggard blob bleakly staring back at me. I'm a wreck. For now. Give me a few years and I'll be coping again though.
Sometimes people find that being at work is respite from their grief - a distraction from the utter hell of living in the real world which brings nothing but painful thoughts, memories and a seemingly endless list of family and friends to inform and practical jobs to be done when someone close to you has died.
Other times people find work is just impossible and the emotions of grief preclude any constructive activity. If in addition you have experienced the exhaustion of a bedside vigil, hospital visits, organising a funeral, and even the idiotic things like going to your deceased parent's house to empty the bins and water the houseplants or tend to the cat... it is just so much. Work can be unbearable on top of all that.
So it's on you to tell your company what you need. Understandably you feel angry right now, but simply inform them what needs to happen, then make it so.
Maybe as a result of this you will be so angry you will do a better job of asserting yourself so you arent exploited and taken for granted so much in future.
Good luck. X