T.V.
H.,
Since you already have a full time job and your parents are willing to give you help to have your own place, I suggest you graciously take their offer, keep your job and find a modest place of your own for the time being.
Two months is a long time to be a house guest and/or roommate no matter how large your parent’s home may be. Nor does it matter how rich or poor they are, they are entitled to their privacy and lifestyle.
They can still be there for you; they just don’t want to live with you and seem to be willing to provide you the means for you to have your own place.
It might be a little difficult at first, but if you want your independence and want to be the primary care taker of your child, you will have to learn to stand on your own two feet.
Blessings....