It is up to the in-law parents on both sides to start building the relationship. It is hard for the kids to know what to do. How can they possibly know what to do in order for you to like them? It is up to you the parents to love them right off the cuff because your children have chosen them and your children love them therefore you must as well. It is up to the in-law parent to make them feel welcome and wanted and to NOT be the source of machlokes between your child and their spouse. Your child’s happiness and shalom bayis is of the utmost importance especially during shana reshona but in general all the time. If you have an issue do not take it up with your child. Do NOT in any way put your child in the middle and make the child choose sides. Try to work it out with the in-law child because it might vey well be just a misunderstanding. Put your cards on the table. Do not accuse, speak about feelings. Say that you want to clear up an issue before it becomes hurtful and runs out of control. If you put your child in between you might not like the side s/he chooses and that will only make things worse.
Always try to dan l’kaf zchus after all you are older and wiser, they will eventually learn, but on the other hand, don’t make yourself into a shmatah. Make sure you are respected at all times. Don’t treat one child’s children (grandchildren) different than any others. All grandchildren are the same. Don’t treat one in-law child different than the other, they are all the same. Of course you might have a different relationship with one than the other because of different personalities but if you buy gifts for one you have to buy for all. Don’t play favorites.
Okay, BH, where do I fall in, in the Shviger category?