First, it sounds like you are being taken advantage of! When taking on other employee's responsibilities, no matter who they are related too, you should be compensated. It also sounds as if you are already having difficulty juggling the tasks you are responsible for. While it is nobel of you to offer to pay for the material, it may be seen by your coworkers as "sucking up" and if your boss does happen to allow you to pay for the material, he will expect you pay for every other mistake you make from here on out. Generally offering to do that kind of thing, while it eases your conscious, is a leads to trouble in the future.
Have you talked to someone in human resources? If not, and you have a HR department, definitely consider talking to someone about your employer's relative. Chances are if he is asking you to carry some of his weight he is probably asking other to carry weight as well. Long story short, if your employer is dedicated to superior customer service, he won't want his relative handing off his responsibilities. Wow.. I mean if I were that customer and I knew the gentleman I worked with had passed off something that was important to me to someone else, I would feel like my business wasn't valuable to him.
You could try talking to your boss from this perspective. Instead of placing blame (or accepting all of it) explain that in the best interest of the customer's needs you think it is important that each employee handle their own tasks. Don't under value your work, because it is YOU! the receptionist who is usually the first person who the client encounters and YOU provide the first impression-- YOU set the bar for the customer's interpretation of other employee's.
I know when I walk into a office and I see a smiling, friendly, and helpful receptionist who truly cares about my needs, I expect ALL the other employees to be the same way. If they are not, I don't blame you.. I go talk to you about how my needs were not met.
you are usually the first and last person customers talk to and that makes you the face of the company.. believe it or not.
I would be assertive in letting you boss know that you are dedicated to the customer's he serves, not the employee's he hires. If you are unable to do your job, A VERY IMPORTANT ONE

, then you need to be able to focus on your work.
If you can explain the situation to your boss in this way he should be receptive.
Honestly, working in an environment that takes you for granted freaking stinks! I'm sorry! I've been in a similar situations. Although I don't know exactly what you are going through I can imagine how you might feel overwhelmed and anxious right now. Take a breath. Remember that it isn't high school any more. If your boss and his relative give you a cold shoulder, hold your head high and let them be immature about it.. And if they do, maybe look into a new career. There are a lot of good companies looking for someone just like you!
Keep up the good work.