Catholic brides of any age come of their own free will to be married. Their fathers, brothers, sons, whatever may or may not escort them. For that matter, parents (mom, too) of both the bride and groom are welcome to walk up the aisle with their children. But brides are never “given away” as if they are property of another person. It has to be her decision. That’s why there’s no, “Who gives this woman?”
As to whether the OP’s MIL should marry this guy- it’s up to her and the old dude. If there is no impediment to the marriage per the “usual”, MIL has the right to request a dispensation to marry him, and marry him if given within the time frame allowed by the diocese.
The OP and her husband are not going to be able to prove she is marrying the guy for his money. It doesn’t matter how well-intentioned they are. It doesn’t matter if they are right about her. To ask to discuss the matter with her priest, as if she is a minor child, is really not a good idea, just makes the OP and her husband look bad. Moms is well over 18. She can do as she likes, including be an alleged golddigger if she chooses. It will not reflect badly on the son if she does.
OP can pray that if this marriage is not of God’s Will, something will happen to stop it. OP and her husband can choose not to attend, but they’d be better off for family harmony if they did.
You just don’t know. Maybe her intended is happy to leave his money to her. Maybe he knows she is an alleged golddigger, and it doesn’t bother him. Maybe he has his reasons. Maybe he’ll make her sign a prenup.
But the woman is more than a grown-up, and more than entitled to do this, even if what is said is true.