L.C.
I'm thinking that they're not "ready" to go to bed because their naptime is a little late in the day. I would suggest making their naptime right after lunch. I would also suggest limiting their naptime to no more than 1 1/2 hours. That way they'll be tired again after dinner and baths. I've found that bathing my kids just before bed helps them relax and they fall asleep more easily.
As far as the temper tantrums go... the best thing is to NOT GIVE IN. Once you start giving in, it teaches them that throwing a fit is how to get what they want. Do not reward a tantrum. I know it's so hard to listen to it. My six-year-old still screams and kicks and cries and if we're in the car, it's nearly unbearable. Also, do not lose your temper with them when they throw a fit. It's still attention (even though it's "bad" attention) and kids CRAVE attention in any form. If you stand firm and don't give in and don't freak out, then eventually your kids will get the message that they're not going to get what they want by behaving this way.
It's kind of an unwritten law that grandparents spoil their grandkids. It's like their JOB. I believe that it's fine as long as they aren't UNDERMINING your authority with your children. You and your husband should have the final say when it comes to your kids.