Dealing With In-Laws After Divorce
Yes, it is definitely appropriate to be in touch with your former in-laws, and it is the best possible situation for your children. The marriage has ended, but your children are still part of their dad's extended family. Your former in-laws are probably savvy enough to know that if they want to continue to have a relationship with their grandchildren, keeping on your good side is essential. They probably are well past any anger or fault finding and are anxious to put the whole divorce business behind them.
Children can never have too many people to love and care for them. Every loving adult brings some special gift to a child's life. You don't want your children to lose out because you feel a bit uncomfortable talking to your former in-laws.
Your in-laws may also love you. They may be heartsick that the marriage ended and still consider you a daughter. Of course, they may also a bit curious about what you are doing and if you are dating. It is up to you, however, to set the limits and share only the information you wish for them to know.