@Cocomarine sounds like a thoroughly decent person and one with the emotional maturity to cope with a tricky situation with aplomb. 
I suppose it's now (thankfully) quite rare for anyone in the UK to be widowed before old age. In previous eras people had to negotiate this all the time. By contrast, it was also far rarer to be divorced or separated.
Now we have the reverse position, so maybe people are automatically assuming widows and widowers still grieving for their deceased spouse are like people still pining for an ex after a relationship breaks up.
But it's not the same thing at all. If a marriage or relationship ends because one partner/spouse dies, it's not happened by choice. If the couple break up, at least one of them has decided that's what has to happen.
(I'm skipping over those awful cases where the deceased died at his/her own hand or as a result of doing something reckless, and the surviving partner has to contend with anger about that as well as grief.)
Also, where children are involved, it's very likely that the widow/widower will be in touch with the deceased's family for the sake of keeping those bonds with the children. They will be grieving too and will naturally be talking about their lost loved one.
If you can't cope with all of this, don't marry a widow or widower. You won't be able to give them and their children the emotional support they need.
We often see on MN posts from adult children whose parent has married again after being widowed and the relationship with the children is suffering because the second spouse is hostile to them, or just not that interested, and the parent goes along with that. In the worst cases the second spouse gets everything in the parent's will and the children get nothing. Very sad.