My husband's ex-wife & her husband adopted our 2 grandchildren, can we contest the adoption?

 Yyou should consult a family law attorney about your legal options and rights, if they are being witheld. You said nothing about whether you had discussed this with them , the adoptive parents, and whether you are already welcomed to visit and keep a relationship with your grandchildren. And if  you want to contest the adoption itself, again, consult an attorney. My guess is that there is a period of time before it becomes permanent, when changes may be made , or the adoption revoked, but after then, its permanent and not contestable. That's a guess. This is a legal matter, so ask a lawyer where the adoption is .

You are too  late.  Why on earth did your husband wait until AFTER they were adopted by his ex and and her husband?  They are now THEIR children and her parents and his parents are those kids' grandparents.  You two could have contested it early on and could have asked for grandparent rights, but not AFTER they have been adopted.

There are two ways to go about this. One is the legal path, which is very complicated. As others have said, state laws vary, and a legal custody fight can not only cost a fortune, it can have a very negative affect on the children. If what you want is visitation, a better way to go about it would be through your daughter and the adoptive parents. They may be willing to see that it is in the children's best interests to keep a connection with both sides of the family. This whole situation is a tragedy for these children, and I hope you recognize it as that. 

This is dependent on state law and may also depend on other factors, such as whether or not you had a close relationship to the children before the adoption. You really, really need to speak to an attorney. Most attorneys will answer one or two simple questions, free of charge, over the phone. From there you can decide whether or not to proceed with legal steps.

But before you go the legal route, have you tried simply asking the adoptive parents whether you can have frequent visits with the children? If you can get what you want (remaining an important part of the kids' lives) without going through legal channels, that may be easier and cheaper in the long run. (Sorry if I'm pointing out the obvious here. Maybe you've already tried this, but if not, it's something to consider.)

In some states,  the right of grandparents to see their grandchildren has been recognized in law.  You should check with an attorney to find out what your rights are in your state.

Since his daughter is ill with bone cancer,  I hope your husband is supporting her and making sure she knows he wants to be an involved parent AND grandparent.  

The courts generally hold that the legal (biological or adoptive) parents have a superior right to raise children without interference. The termination of the mother's parental rights by an adoption can also sever the other maternal relatives' rights. Google [your state] adoption termination of parental rights.

As someone with no legal experience and no knowledge of all the facts you left out, I hage no idea. See a lawyer.

Can you? Sure. Will you win? No. There are no such things are grandparents' rights in law unless the grandparent is exceptionally active in raising the child, as in a full time carer.

Why don't mind your own business