first one should be correct. I think the second one should go like this: Mr. Green was very glad that her daughter won the first prize in the singing comeptition.
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wangqh2696122I am so glad that you have succeedThese are both fine for me in casual use. I use "so" to mean "very" in this way.
Mr. Green was so glad that his daughter won the first prize in the singing competition.
wangqh2696122I am so glad that you have succeedI am so lad that you (have) succeeded.
wangqh2696122Mr. Green was so glad that her dayghter won the first prize in the singing competition.Mr Green was so glad that his daughter won...