This has been a challenge for many in the last 10 years or so. Some of newer hardware from Cisco and other vendors addresses it. For example the 3750 stack switches, if one of the members fails another will take over. But from what you are describing, a child switch shouldn't affect any one else unless there is another switch dazy-changed off it. Best practice is to have each switched home-runned back your 4510r.
What if the 4510r fails? To solve this you would install another switch, and setup HSRP between the two for all the VLAN's. Also, setup dual uplinks from the child switches, one two each parent switch. Make sure you have spanning tree enabled setup correctly! If the child switches are L3 capable, then you can also build this using a routing protocol on the uplinks instead of L2 and spanning tree.
Hope this helps and gets you going.