She is a talented woman and she no doubt can decide what is best for her, you and the T don't need to do that--especially after a mere two months of dating.

The evidence is that the solution to a specific phobia is not to design one's life around the phobia. So for a person who is afraid of elevators, the solution is not to avoid any building taller than two or three stories for the rest of their lives. That simply perpetuates the phobia. The solution, rather, is to confront the fear and learn through repeated experience that nothing bad happens when they ride an elevator. From that perspective, therefore, the solution for your anxiety is for her to go see her dogs more, and for you to endure the anxiety and learn to trust her through your own experience.

I am having trouble understanding this statement, because it does seem that you explicitly wish to infringe on her freedom to be in contact with her ex and her dogs. It sounds like this might become/may have already become a dealbreaker for you.

In my opinion it oversimplifies to say that kids would be their priority in such a relationship (kids with ex). There would be more than one person to love, no doubt, but love can expand to be shared with all of the beloved people. This happens all of the time in families, ex or no ex. I wonder if you have already discussed your views on having/not having children with her.