1. You don't OWE your parents anything. They chose to give you the money. (Whether or not it was a good idea to accept it isn't the issue anymore because it's all said and done.)
2. If you feel obligated to them because of the money, you could pay it back and that would take away that feeling of obligation.
3. YOU are not responsible for your mother's emotions. Crying is a great way for her to manipulate you, and it's wrong for her to do that. DO NOT feel responsible for her emotions if what you are asking is done in a kind way. (Obviously if you were yelling and saying mean things, that would be another story.)
4. Your mother has no right to tell you who gets to raise your children should you die. That's all your choice. That sounds beyond crazy. However, since I don't know the situation, I would suggest you honestly ask yourself if your mother has a legitimate reason for being concerned about your husband. Is there something about him that makes her worried for your children's safety. Is she worried that without you around he would harm your children? BUT, if it's just that she WANTS the kids for herself, forget that.
5. Suggestions for how to get them to leave your house...
"Mom, we are feeling the financial strain of having two extra adults in the house (food, water bill, electricity bill). We just can't afford it anymore. Do you think two months is enough time for you to find a new place?" If she responds that you aren't working, tell her that you and your husband make plenty of money to care for your family with you as a SAHM. It's supporting two extra adults that is causing the strain.
"Mom and Dad, thank you for giving me that money a long time ago. I can pay it back now, and I see that you need it to get yourself a home."
"Mom and Dad, we are struggling financially and can't afford the current living situation. Would you prefer to contribute to the expenses here, or would rather move into your own place?"
If she tries to go off on a tangent so she can cry (like talking about your kids and the money from the past or the fact that you aren't working) just stick to your guns and don't waver. Say, "That's not what we are talking about right now. We are talking about the fact that we can no longer support two extra adults." Just keep repeating that if you have to. DO NOT let her draw you into arguing on another loosely-related topic so she can have an excuse for crying.
Ask your brother how he got them to move out. He obviously did it successfully. Maybe he could give you some pointers.
Good luck. I hope it works. No fun at all, but you need to do what is best for you, your husband, and your kids right now.