Generally, drinking establishments are free to set and enforce their own policies regarding who they want to serve. There is no law that requires an establishment to let an under age person to sit at a bar or even let them in the door.The fact that they are with relatives doesn't matter at all.
There is noting in the law that precludes them from sitting at the bar with their family members. However, a bar or restaurant may determine their own internal policies related to minors in the bar. There is noting inappropriate about their rules which apparently seek to ensure that minors do not have access to alcohol.
Disclaimer: Nothing in this email message creates an attorney client relationship absent a retainer agreement with this office. Any response to email inquiries should be considered general in nature and should not be relied upon as legal advice. You should always consult a lawyer in your state regarding your specific legal matter. Visit online at http://www.minnesotaLawyers.com
Your question falls under Minn. Stat. section 340A.503. Both Mr. Beaulier and Mr. Kane have given you the correct answer. The statute prohibits a person under the age of 21 from entering an establishment licensed to sell alcohol if their intention is to purchase, to consume, to be served alcohol, or to order the delivery of alcohol.
The statute also provides an exception for those under the age of 21 to enter an establishment licensed to sell alcohol if they are employed there (with certain exceptions), if they are there to eat food, or if they are there for a social function (although alcohol cannot be sold in the area where the social function is taking place).
The statute can be a little confusing regarding the exceptions in the previous paragraph, because it further proscribes local ordinances from preventing those 18, 19 or 20 years old from entering such establishments for the previous resons. What this means, in short, is that local ordinances can prevent people under the age of 18 from entering establishments licensed to sell liquor at all.
By now, you are probably wondering what any of this has to do with your question. Simply, the controlling law on this issue allows those under 21 to enter a bar for certain reasons and not others. The law further prohibits cities and towns from enacting local ordinances prohibiting what the law allows. The law does not establish an underage person's right to enter a bar, and it allows (under certain circumstances) but does not require the establishment owner to permit those under the age of 21 to enter the bar.
Obviously I have yet to learn to be as precise and concise as my colleague Mr. Beaulier. If brevity was what you were looking for, I refer you back to the excellent guidance of Mr. Kane and Mr. Beaulier.