Wow....They sound like they are definitely taking you for granted in a HUGE WAY OP & this is so disrespectful as well as inconsiderate.
You have two options available to you now.
• Have a direct talk w/them that all this cancelling is making a big dent in your job prospects. You reserve those days/hours for them specifically and when they cancel last minute, it can affect your own job prospects negatively.
(Trust me on this one....If the shoe were on the other foot, you would be gone!)
The only way in these situations to do damage control on their end is to compensate you for calling out.
OR ~
• You can decide that all of the stress involved is just not worth it.
You need a family who is much more responsible as well as considerate.
*If you decide to do the latter option, watch them come begging for you with their tales between their legs. :p