How long have you been together ? And do you mean he split from his wife this December just gone , or the December before ? If it was the December just gone I would be inclined to slow down your relationship building with the three oldest . But I wouldn't stay away from the house . I would look for a healthy balance of going out on dates , and going back for coffee . Do you stay over ? If so , id keep the day and frequency the same for a while , so the kids become aware that on this night , you stay over , and they can make alternative plans if they are inclined to .
If it has been over a year since the split , then their dad really must step in when they are being rude and disrespectful . I don't think there is a correct time to be introduced to kids . I was introduced to mine fairly quickly , and we were out doing things straight away . It took me years to develop a relationship with the kids though , that was my choice , I needed to take it slow , but it worked out .
I used techniques such as listening , and watching , looking for snippets of information regarding their interests , likes and dislikes , and when the atmosphere was right , id start conversations based on this . Or id happen to have a dvd that I knew they wanted to watch , or cds that I knew they liked ( Funnily enough we have the same music taste , but I am 11 years younger than DH ) .
I would also think about easy , none full on activities . It's coming up to summer , what about a Bbq , and get the eldest favourite tipple in and a favourite dessert ? Invite friends or their family over . Plan to go see a gory horror movie , and see if the older ones want to join you ? But stay relaxed , don't force anything , be natural , back off and just listen for signs . If the atmosphere is good , make contact , then pull back before they have a chance to get bored or realise they are talking to you . Don't show any weakness either , roll your eyes and walk away if you have to .