Sis insha'Allah I can help you because I just learnt this topic last week.
Talaq raja'in - a talaq where your husband can revert back to you (1 and 2) whilst still in iddah (iddah period depends. i.e. menstruation must be noted, if you are menopausal your iddah is 3 months only. if you are pregnant, your iddah is until the period you give birth etc.) During this talaq, if he reverts back to want to be with you, you cannot refuse him. The only way you can do so is to bring this matter to the shari'ah court and give good evidence as to why you want to reject (i.e. he beats you up, he has been squandering your money, he refuses to let you see your parents etc. but the reason must be strong and valid). Only the qadi has the power to decide, not you.
In this talaq, you can stay under a roof with him. He still has to provide for you and you still need to seek his permission. But the conditions are, you cannot have sexual intercourse with him and as long as there is somebody else (adult) in the house. If your children are grown up (i.e. in their teens, twenties etc. & able to ensure he does not sleep with you) then it is okay. I suggest you cover your aurat at home sis, and if he wants to be with you (perhaps because he wants to sleep with you) which is most likely at night, perhaps you could put it off until you can reject the matter in court
(if you are not willing to go back to him).
Talaq (3)
This talaq he cannot be wanting you back (I am not sure if forever).
Finally,
a woman is not in iddah after divorce when she was married to the man but they had never had sexual intercourse.
(In addition you can also re-marry after your iddah period is over).
Do take care of yourself sis. I am not so knowledgeable and I do not have the sources for these but I'd just learnt it in class last week and want to help you... If you do not want him back sis, please take care of your modesty. I am afraid if he sees you uncovered he would want you back (for the wrong reasons).
Wallahua'lam bishawab