I'm not quite sure how you got your English translation! The sentence "但是如果没有紧急情况，我用钱用得多了，他们下个月就不给我那么多钱了", translated, would be "but if it isn't an emergency, and I use too much money, my parents next month just won't give me that much money".
The two discrepancies between your translation and the English are in "我用钱用得多了" and "就不给我那么多钱了".
"我用钱用得多了" uses the 得 character, to provide description for a verb. You may be familiar with "跑步跑得快“, for example, which would be a way to say "runs fast". In the same way, the descriptive word in this phrase is "多", which describes the verb "用钱", or "spend money". And, of course, "多" means "much", rather than "little". "Spend only a little" could be better translated as "我用钱用得少了”.
The second area of discrepancy is in "就不给我那么多钱了", which translates literally to "just won't give me that much money", where 就 = just, 不给 = won't give, 我 = me, 那么多 = that much, 钱 = money. I would assume this simply means the parents would take the surplus spending out of next month's allowance.
Your translation, translated back into Chinese, would give something more along the lines of "但是如果没有紧急情况，我用钱用得少了，他们下个月就给我一样多钱了".