No one on Avvo is going to advise you to avoid service. In an L&T case, they can serve via "nail and mail" at your residence, so will you get served. As for being underage, you are likely a person of suitable age and discretion, so service on you would likely be proper in any event. As a minor, you won't be a party to the action.
The problem you have is that you're running up against the maxim "Don't pay, can't stay." Avoiding answering the door will only result in nail and mail service. Your mother has to be proactive at finding help through Social Services and or family. The Petition will be taped to the door and mailed to her. She should go to court and tell the Judge she can't afford a lawyer (I assume she's unemployed) and would like to see if Nassau-Suffolk Law Services can help her. Good luck.
I am not your attorney and any posts/messages or responses to posts/messages can not establish an attorney-client relationship. www.PatchogueAttorney.com You should not rely upon free legal advice and I disclaim any liability for the results if you do.
No attorney may assist you in such endeavor. But at a consult he can tell you what due date for service to occur in any court.
This is not legal advise. Office visit for a free consult is needed.