It seems the situation has gone from bad to worse, Deb. I am so sorry. Hugs!
I'm also sorry D has pulled DS into this, only to refuse his suggestion of a sit-down. It is possible a sit-down wouldn't work at this time. Like agnurse, Ive heard of situations where this effort just ended up in a shouting match, etc. But why did D reach out to DS if she isn't going to take his advice? Did she just want to cry on his shoulder? Is she hoping he'll relay messages to you about how she's feeling (as he already seems to be doing) since she won't talk with you herself? That suggests to me she does want some contact, after all, if only to express her feelings. But, IMO, it's immature of her to involve a 3rd party/her brother.
Perhaps the gift was also an overture and she was hurt when it was rejected. Maybe she was trying to begin to rebuild the relationship between you two and herself before including the kids. But after the way she has been acting, how could she expect you to know that?
Still, I feel she does want to resolve the issues (whatever they may be) and resume contact. So, IMO, there's hope. But I think it is going to take a while.... Patience...
Meanwhile, I'm glad your seeing a solicitor. However, like Peony, I think you should just hear what they have to say and mull it over for a while. Please don't act in haste or anger.
As for DS, I think he should let D know he can't be in the middle of this. But that's up to him, of course.