If you wait until you are legally able to get a tattoo without parental consent (aka when you're 18+) and you save up all the necessary money needed, it's literally no one else's business.
Sure family members and strangers can have opinions, but sometimes, it's best to keep those opinions to YOURSELF. There is NOTHING wrong with tattoos whatsoever. People get them for many, many reasons.
Tattoos will NOT prevent you from getting a job. I actually had a teacher when I was in about 5th grade who had a tattoo on her ankle. She always loved to wear dresses or skirts, so the tattoo was always visible. Not a word was said and she was an amazing teacher and very kind lady. If your school was different, you could always wear maxi skirts, long dresses, or pants to cover leg/ankle tattoos and long sleeves or light sweaters to cover any arm tattoos.
It's wonderful your mom will not judge her children if they choose to have tattoos, even though she personally does not care for them. THAT is being a good mom. She may not like them herself, but she will not judge those who do choose to have them. Good for her - be thankful you have a good, non-judgmental mom.
As for your dad and other family members, it's really none of their business. If you're an adult with your own money, NO ONE can tell you what to do. If they make rude comments or make a huge deal, tell them to back off and mind their own business. Let them know getting a tattoo DOES NOT change who you are. You'll be the same person after you get your tattoos that you were before you had them. Whether you have tattoos or not means nothing as far as the type of person you are is concerned.
As far as telling them, well, that's up to you. I'm sure they may find out eventually depending on where the tattoo is located. I say just don't bother. Get what you want and if/when they see it, oh well. Play it casual. When someone sees it and points it out, just be like "yeah... it's I have a tattoo, so?". Make it known YOU are in control and make your OWN decisions and that you don't care whatsoever if they "approve" or not. If they complain or try to trash your dreams regarding work, THAT is an easy fix - just go out and prove them WRONG. Go out and find a good job you're happy with. Then, when you get it, give them the "I told you so" smile and go on.
Good luck - I really hope you don't run into too many issues over this and your family members choose to behave like mature adults when they find out.