This can greatly depend on your relations with the family member in question, and your own comfort levels.
On the one hand, your family-member client coming to you for assistance can point you to areas in your documentation you need to expand.
On the other hand, a family-member client who expects a higher level of support than your other clients because they're family and know how to contact you wherever whenever...yes, there can be a definite problem.
If it's possible to make it clear to them that they're more than welcome to ask for assistance whenever they need it but they need to use the same support channels as any other client, AND will be bound by the same rules as any other client, no problems. If they accept these boundaries, and you feel comfortable that they'll stay within these boundaries (largely), then good: you've got a client who may be an early alert to potential problems that you might not hear of from your non-family customers, but you've also got a paying client.
Inevitably, they will try calling your personal number, trying to buttonhole you at family gatherings, et cetera. (Same thing happened to me.) The first few times, answer their question and remind them to submit a support ticket / post in the forums / whatever, just like you would your other clients. If they continue to try and get special treatment despite reminders, suggest that since they want different support than you provide, that they might be happier hosting somewhere else. Give them a few URLs, tell them things to watch out for (unlimited everything, hidden "gotchas" in the TOS), and give them 30 days to find a new web host or to stop demanding special treatment. (After all, you'd say the same thing to a client who demanded service / support above and beyond what you were willing or able to provide, wouldn't you?)
Just like any relationship, you have to lay out the ground rules. Make sure both parties know what to expect. Let them know, right up front, that if you find that they need more support than you provide your other clients, you'll either charge them extra or you'll encourage them to find another provider. If they know that up front, either they'll be disappointed that they don't get special treatment and they'll go elsewhere...or they'll know that they'll be treated just like any other client, they'll respect that, and you'll gain another client.