For describing a verb in Chinese, you need to use "地"
Such as what you said "妈妈高兴地笑了"
"得" is used to connect verbs and adverb.
For example, 跑"得"很快 or 读得很慢
or you can change to 很快"地"跑 or 很慢"地"读
I know it is difficult to distinguish "地" "得" "的" in Chinese.
But for native speakers, we sometimes mix them all.