kaette kite

I’d Really Appreciate It・たらうれしい

とうれしい and たらうれしい are similar phrases with slightly different nuances and conjugations. Generally, they both are a polite or indirect way of requesting something, much like “I’d appreciate it if you could….”
たらうれしい is more common.

とうれしい is just added onto the end of the sentence and is like, “I’m happy/glad you….” like it, agree, came to my birthday, etc.

たらうれしい deletes the ending of the verb and replaces it. It’s more like “I would be happy if / I hope you…”

For both phrases, they usually have くれる before them, which means “give me.”

私は彼を支えてくれたら嬉しい。Watashi wa kare o sasaete kuretara ureshii.
I’d appreciate it if you supported him. (If give him support, I’m happy.)

その写真を送ってくれたら私は嬉しい。Sono shashin o okutte kuretara watashi wa ureshii. 
I’d appreciate it if you could send me those photos. (if send me the photos, I’m happy.)

早めに帰ってきてくれたら私は嬉しい。Hayame ni kaette kite kuretara watashi wa ureshii.
I’d be happy if you could come home early. (if coming home ahead of time, I am happy.)

手伝ってくれるとうれしい。Tetsudatte kureruto ureshii.
I’d be happy to have some help (but you don’t have to if you’re busy). (If give me help, I’m happy.)

気に入ってくれたら嬉しい。Kiniitte kuretara ureshii. 
I hope you like it. (if pleased, I’m happy.)

私と会う時間を作ってくれたら私は嬉しい。Watashi to au jikan o tsukutte kuretara watashi wa ureshii.
I hope you can make time to see me. (if make time to meet with me, I’m happy.)