No matter the activity, Timothy jumps right in. 
Ariel is a little more timid but willing to try new things. S
he does well socially which is one reason she likes school..

Both children want a family that is active.  What they both need is a family that is patient, structured, and loving.  A two parent family with a strong father figure would greatly benefit both Timothy and Ariel.  

The children are bright and love each other.   But they've been hurt and need parents who can help them control their emotions and let them express their feelings.