Ryokoさん's answer is very good. In addition to that, I'd like to answer from a view of grammar. もつis equivalent to "to take/ grab/catch" in English. もつis a momentary verb瞬間<しゅんかん>動詞<どうし>. It's not a continuation verb継続<けいぞく>動詞. So You have to use te-form and います. "have" is a continuation verb. example situation: When a rich woman with many baggage arrived at a hotel, the porters helped her. And one of them said "いちばん　おおきな　ものは　わたしが　もちますI'll take the biggest one". On the way to her room, the woman asked "who has my biggest baggage?" The porter answered "わたしが　もっていますI have". ※At the final sentence, わたしが　もちます is incorrect. もってto take + いますstill being ＝ I took it and keeping it ＝ I have　※a continuous movement います／あります is a state verb状態<じょうたい>動詞. It has a continuous meaning from the beginning. So you don't have to use te-form. I mean you cannot use it. I have an older sister and a younger brother. わたしには　あねと　おとうとが　います／あります。correct わたしには　あねと　おとうとが　いて　います／あって　います。incorrect わたしは　あねと　おとうとを　もって　います。correct わたしは　あねと　おとうとを　もちます。incorrect もつcan be used "to have" in classical style. かれは　10<とお>の　かたがきを　もつ。He has ten titles. かのじょは　さんにんの　こを　もつ　シングルマザーである。She is a single mother who has three children. for reference: かのじょは　らいげつ　けっこんします。She is going to marry next month. かのじょは　けっこんして　います。She is married.

We have various translations for "to have". It's very dofficult for me to explain about it without using Japanese sentence. Please review this when you can read them and understand them. By the way, please don't separate もって and いる because IN THIS CASE, もっている means "to have". In my opinion, remembering the translation もっている for "to have" for "to own objects" would be better. Please remember that there are cases that each words don't have the specific translation and each language has its own way of saying. Anyways, here are the basic and most common examples. "To have" for the person, we say いる/います. I have a younger sister. = 私には妹が一人います。(わたしにはいもうとがひとりいます。) I have many friends. = 私にはたくさんの友だちがいます。(わたしにはたくさんのともだちがいます。) For pets, we say 飼っています(かっています). I have dogs. = 私は犬を飼っています。(わたしはいぬをかっています。) For the object, we say もっています like "to own". I have a book. = 私は本を持っています。(わたしはほんをもっています。) Like "there is/are", we say ある / あります. My city has a big park. (There is a big park in my city.) = 私の町には大きい公園があります。(わたしのまちにはおおきいこうえんがあります。) Other example: May I have your name? (Please tell me your name.) = おなまえをおしえてください。 Please get accustomed to the Japanese language step by step. I hope this was helpful.

もっている is the progressive form of もつ. You wouldn't say もつ unless you have a sister in the same way you have/own a pencil. もつ can also mean "to borrow/to hold", depending of the context. かぞく　に　は　あね　と　おとうと　が　いる。 I have an older sister and a younger brother in my family. (Literally: As in (my) family, older sister and younger brother exists) Well, I'm not a native speaker so correct me if I'm wrong! ^^