Because of having a lot of difficulties, she managed to sell the house.
-> As she had a lot of difficulties, she managed to sell the house.   
She is proud of her priof (This seems to be a typo. If you meant "prior" or "proud," you would use those words.)
If you meant "prior," the sentence would be: "She is proud of her prior achievements."
If you meant "proud," the sentence would be: "She is proud of her accomplishments."
What about going for a picnic this weekend? (picnicking is not a correct word in this context) -> What about picnicking this weekend?