I grew up next door to Fall River (Assonet), so I know where you're coming from.
Seekonk and Rehoboth are pretty different from each other. Both are safe, family oriented communities, but Seekonk is much more suburban than Rehoboth. I don't think the schools in either community are ultra stellar, but they're not bad. Certainly better than Fall River's. The high schools are Seekonk High and Dighton-Rehoboth. DR is a bit of a drive from certain parts of town, but it's a nice school. Seekonk is nice too.
Like I said, Seekonk is more suburban. While it does have some newer homes, many are similar to what you see in Somerset (1950s-1970s style ranches and cookie cutter neighborhoods), not strikingly attractive. You are closer to box stores and suburban retail along route 6 and of course, you have Providence Place Mall just minutes away from Seekonk. Everything's a little further from Rehoboth, but not outrageous.
Rehoboth always surprises me. The first impression I usually get is from all of the run-down or abandoned retail along Route 44. However, when you actually get off that road and into town, there are some real attractive areas. Personally, if it were between the two communities you've listed, I'd go with Rehoboth. I have a good friend who recently made the move from Fall River to Rehoboth.
I agree with the above poster who suggested Bristol, RI. I'd also ad Warren RI to the list. Both communities are very pretty. Again, schools aren't wonderful, but they're not bad. Your children won't be at a big disadvantage by attending them. I would choose Bristol or Warren over Seekonk or Rehoboth any day.
My question to you is, how certain are you that you'll be working in Providence? Is this potential move something that could happen soon or are you just thinking about your potential options. The reason I ask is because Providence isn't an easy place to get a job right now. I'd make sure you've got one locked up before you invest in a move.
I'd use a MLS search to get an idea on the housing market in either community. I'd guess that Seekonk is similarly priced to Somerset, Swansea while Rehoboth my be just a little more.