Can disease resistance from vaccination be inherited?
Not usually. I say usually because there's a fairly new (~15 years old) branch of genetics known as epigentics which has been shown to allow for inheritance of acquired traits. So it's possible that if the way in which a vaccine worked was altering your epigenome or genome, that it could be passed down to your children. However, that's just a hypothetical since none of the vaccines that I know of currently work in that way, but maybe something in the future will.

As of now, vaccines generally give you immunity by introducing some portion of the virus you're vaccinating against and "sensitizing" your immune system against it. This could be the viral envelope, it could be viral DNA/RNA, could be a viral protein, etc. However, in all of these cases, your immune cells are carrying out a fairly complex process in which they make antibodies with an almost random pattern constantly, and when one is produced that binds to this virus, it tells the B cell that produced that antibody to start making more. In this way, it "confirms" that this B cell is onto something. 

Having said that, the B cells themselves are not passed on from parent to child, so a child would not be permanently immune to a virus even if the parent was. BUT, some antibodies can be passed from mother to child through the umbilical cord. These antibodies have a finite life and since they're not cells, they don't replicate and device. So the child would be immune to whatever a given antibody works against as long as that antibody remains in their system (usually on the order of weeks to months). Once the antibody is degraded, they no longer have any immunity, just as their parents did not have immunity before being vaccinated.