My parents have been divorced since I was two. My mom, brother and I lived in a different state than my dad, therefore, my mom had to do the leg work with a lot of things in regards to us kids and then tell my dad to get his input. His response was always 'I trust you make the right decision for our kids' and he was right. My mom never deliberately put us in harms way and if decisions were made that turned out not so good, she pulled us out.
So assuming Lexie's dad thinks Dina is a good mom, he may not be all that concerned about the details (like my dad wasn't) because he trusts Dina is going to do right by Lexie. Doesn't make him a bad dad.