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-What are your ages?
-How long have you been together?
-How long was he married to her?
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Thrity years is a long time to be with someone and it's not like they divorced she died he may have very well have spent the rest of his life with this woman and since she has passed on she isn't really a threat to your relationship. He may be wanting to do this so that he doesn't disrespect his wife's memory or his children they might ask questions if they see no memory of their mother at all, he may be doing this out of respect for his children losing their mother. Maybe you can compromise and he can put it in a draw somewhere and only get it out when the children are there. You have to be very careful that you don't make him resent you for making him try to forget all about his first wife whom he had children with.
No matter whether he has the picture up and out in the open or in a draw you can not erase the memories they had together he is with you now and there is no way this woman can come in between the two of you he just doesn't want to let go of the memories he had with her and the beautiful children she gave him. It's just like if a person lost a family member and they want to keep the memories they save something from that person that will remind them of them from time to time. Ex husband's are one thing but this is someone he loved that died they didn't get divorced. Maybe try to work out a compromise to only put the picture out when his children come to visit or are there unless they live there with you then you will have to accept him having a picture of their mother on the wall or the children may resent you also.
That is why I suggested a compromise but his children even if adults would be offended if they knew you wanted no memories at all in your home and are trying to make their father erase all memory of their mother. You have a right to have input on what goes and doesn't go in your home I'm just saying you need to be careful it isn't taken the wrong way. This is something the two of you are definately going to have to work through before you get married and move into your own home. Tell him that you feel that this is your (yours and his) new start and you do not want anyone old memories you want to start new memories with him and that you're not trying to disrespect his wife's memory but this will be your home together not yours, his and his first wife's maybe then he will understand why do not want her picture in your home that you will share with him.