Brysing is right, since you are still pretty young, you should just drop this subject if your mom doesn't approve. The craft will be here when you are allowed to come back to it, if you still feel the draw to it. You should respect your mothers wishes, and when you get a little older, you can explain what your religious beliefs are to her.
You should respect your mother's wishes. I have found that an alter is any space that you set items that are special to you. Even a small shelf with a few decorations can be an alter. There is so much symbolism in the craft that you could make an alter in plain site that your mother would not even know was an alter. Flowers are so lovely and a representation of the beauty of mother earth. An image or item that has a sun on it is a representation of the god. Just keep it simple and cheerful. You will know what the items are for but your mother will just see them as decorations.
Of course, at 20 years of age, there is a difference. I take it that you still live with your mother? If your mother objects to the way you wish to live your life, leave! But talk it over first. Your mother may not have the same beliefs as you, but you must try to explain that you have your own beliefs and, as you respect hers so she must respect yours. Approach this gently of course, not aggressively.
As kts said, an altar can be anything, and easily something that can be seen as "simple" decorations.
Also, an altar is only to help the power to you. Any kind of spells etc can easily be done without an altar.
if you cant have an altar, its best not to have one for the time being, until you can. i didn't have an altar for about a year, so i made one and it "blends in" with my room. my parents have not noticed it to my knowledge, only my boyfriend has realized it was an altar. an altar doesn't have to be as decorated or ordinate, it can be as simple as a Candle, and a crystal, to as intricate as you want but even something as simple as a candle can be an altar. its not always necessarily to have one, but i feel very calm and happy when i am in front of mine. it is always an option to at least try to talk to your mother about it calmly.
you can have an alter outside in a wilderness location.
also I've been doing magic for over a decade without one.
my main magical tool is my magic-spell book,
which is a journal I write in.
I keep my sacred object on my table,
but I consider then as grounding objects,
for quantum entangling with those vibrations.
For instance I have a buddha for meditation,
an Egyptian head for teachings of Ra,
I also love granite rocks,
here in Canada some are billions of years old.
I also carry ritual stones and objects in my pouch,
which could be your purse.
I would suggest you magic-spell cast for acceptance,
can also cast for a place to live and practice.
my parents really didn't like me living there,
so I cast spells for a new place,
and now been here for two years,
with the partner I cast for,
and life is paradise :-).
