If the chain link fence is on the property line then you share it. You CAN leave it there and put the wood fence up on your side. You can also set the wood fence it by about 3' (enough room for you to get a mower thru

) and then their kids can't get on it by way of their chain link fence. Just make sure if you do setback your new fence you do NOT give up that strip of land. Maintain it yourself. Put some nice cacti in there if you want with some gravel and don't worry about mowing it
Now, if they taunt your dogs enough I'd call the police non-emergency number. Let them come out and instruct the sorry butt parents and grandparents that if something happens to one of your dogs it is on record that they have been causing problems and teasing/taunting them.
I'd go ahead and fence in your ENTIRE yard so these kids can't get into any part of it.
There is one fence guy out there that I've seen do good work. His last name is Blackwell, I think. Sunnyvale Fence is another close by one in Garland on I-30 and then there is Southwest. Check on doing a fence made of HardiBoard and Hardiplank. AWESOME fence and doesn't need replacing like a typical wood fence.
