There is a lot to unpack here.
1. Consider the fact she is a barren woman, no decent man would accept her the way she is. If she were to marry someone, odds are its to someone who would definitely beat her for being barren. The Crown Prince gave Yvette a man who he knew wouldn't be abusive towards her just because she is unable to have kids of her own. She also never knew she was barren and I half expected people would say she is faking that she didn't know but pleasantly surprised that wasn’t the case. If you think about it, it hurts that Eldred did know she was barren and didn't tell her.
2. The age gap, sure its huge, its historically accurate given the time period they are in. Plus, the Grand Duke was her best option, only option even. Yeah, there was harmful hurdles in the way but things finally settled down for now and the children are accepting Yvette.