New relationship

Hello I am new to this forum and have never used a forum before so I would appreciate some tips.  I have been seperated from my ex for 21 months now and am currently going through a divorce.  I dont get on with my ex as he talks to me like I am a child and what ever I say is wrong as far as he is concerned.  I have custody of the children ages 12 and 8.  I have a question if anyone can give me some advice on what to do;

I have been seeing someone for five months now and both the children really like him, they have met his son and get on with him well often asking if we can visit them.  My daughter in particular was really happy with my boyfriend and often gave him cuddles and enjoyed the attention.  Now she is feeling guilty of the time she spends with my boyfriend because she feels sorry for her dad. (He has had a girlfriend since before we split up)  She can be ignorant with my boyfriend and has said she does not want him to call her E (her name) which we all call her; she does not want him to call her 'honey' either, which he calls most girls.  I have no concern of any problems with my boyfriend’s relationship with her as he has never been on his own with her.  What can I do as it makes me feel really nervous when I mention his name as she rolls her eyes and says do we have to go to 'name' (my boyfriends), why is 'name' (my boyfriend) coming to Granddads birthday meal etc?