The biggest difference between 帰る and 帰り is that 帰る is verb, but 帰り is adjective or transformed noun. In case you use 帰り, you need to put verb in that sentence.

[帰る]（to return) is an u-verb. Therefore, it changes to り in ます and たい form. [帰り]ます（to return (polite)) [帰り]たい(です) (to want to return) Similarly, [行く] to goー＞[行き]たい、[買う] to buyー＞[買い]たい、etc. I hope this helps some!

Kaeru conjugates in that way. There are many other verbs which conjugate in the same way. For example, 走る　走りたい,　触る　触りたい,　借りる　借りたい, etc.

This changing is called "五段活用(godan katuyou)、連用形(renyoukei)" in Japanese. When you use "～したい（means want to do）”,you need to change verb's last vowel into "い(i) sound" or "え(e) sound". I show you some instance. ---------------------------------------------- 寝る(to sleep)→寝たい(want to sleep) neru →n"e" + tai 食べる(to eat)→食べたい(want to eat) taberu →tab"e" + tai 行く(to go)→行きたい(want to go) iku　　　　→ik"i" + tai 見る(to see)→見たい(want to see) miru　　　　→m"i" + tai ----------------------------------------------