How can I convince my mother-in-law that she needs to go to assisted living?

Does she have a sound mind? If so, it’s her decision whether she moves or not. You can only give her your reasons for thinking it’s a good idea, but the choice is hers. If dementia is involved, whoever has POA for healthcare can use that to help in getting her moved, but it’s still a process she may fight

Maybe do a virtual tour of places. So when you give her a reasons to go there,she can see for herself.

If she is still of sound mind, it's her choice.

Is she living with you? Are you stuck taking care of her?