、。
She welcomed me so warmly that I quickly opened up to her.
Literal
She [topic-は] me [object-を] from-the-heart welcomed [for my benefit-てくれた] [because-ので], I [topic-は] quickly her [with-と] opened-up.
心から ('from the heart, sincerely, wholeheartedly') is a stock adverbial — から here in its 'from' source-marking sense, applied figuratively to one's heart as the source of the warmth. ~ので connects the two clauses with a causal nuance softer and more objective-feeling than から (the conjunction). 打ち解ける is a beautiful native compound: 打つ ('strike') + 解ける ('come undone, dissolve') — literally 'strike open and dissolve' — meaning to drop one's reserve and become close. The と marks the person you're opening up to, in its comitative 'with' sense.