Are the top/sides and neck intact?
I’d get a second quote. $1500 isn’t sneezing-at money. Also, I’d ask those that know, “is it going to be worth it to repair it?” I might ask around to see if there is a guy or gal who is considered “the” guru. I know when it comes to guitars, I wouldn’t want just anybody tackling a project like that. I want the person who makes magical things happen with wood.
With all that said, I played violin as a kid. I haven’t kept up with it or gotten back into it (yet). However, I am around them enough through my fiddle playing buddy to know, if it’s a nice violin, $1500 is not a huge amount of money. To purchase a “nice” violin, the local violin builder/repair guy says you will be looking at $3k and up. I am thinking it well could be that if you restored it, it might be worth significantly more than what you will have in it. And all of that ignores the fact that it was played professionally by someone in your family many generations ago. I don’t know that we have enough info to make the call, but I am leaning towards “go for it.”
By the way, if you think picks are expensive, wait until you start looking at “nice” bows. From what I have heard, they make a world of difference in tone though. Pro level bows are graded as they are made and priced accordingly.