Legally there is no issue. It is your work. You own the copyright. You can licensed anyone you like to make copies no matter how many copies have already been made (subject, of course, to any rights you have already sold).
The issue is going to be what individual publications are willing to accept. Each publication can set its own policies about this. By and large I think these will be set by one of three factors:
Pride. The publishers of small hobby mags that don't make any money often seem to want totally pristine stories that have never appeared anywhere in any form. As far as I can tell, this seems to be purely a matter of pride. The individual sales of these mags is so small that it is doubtful that publishing something that has already been read by 50 people elsewhere is going to have any impact on the current mag's sales. But this kind of publishing is mostly about vanity, where the vanity the publisher is seeking is potentially making a "discovery". So it is not a discovery if it has been published elsewhere.
Exhaustion. Publishers may hesitate to republish something because they fear that the previous publication has exhausted demand. All the copies that can be sold have already been sold. This is unlikely in the case of blog only read by family members -- unless the work is not good enough to be read by anyone other than family members, in which case the issue is moot since there is no money to be made by publishing it anyway.
Platform. On the other hand, successful prior publication can establish the demand for a work. This was the case with my book Every Page is Page One. Most of the book was first published on my blog and I was able to demonstrate demand and interest in the subject matter based on the viewing figures and the wealth of comments the blog posts attracted. This is often called "building a platform" and having built a platform can be a great asset in getting a publishing deal. (It is worth noting here that some successful self-published works get picked up by mainstream publishers because they see the demand is there and that the author has built a platform that can be used to sell this and subsequent works.)
So, your blog posts could be a hindrance or a big help, or essentially irrelevant, depending on the nature of the publishers interest and the type of rewards they are looking for when they publish.