The OP does not have AA miles, and does not have any credit-card points that convert directly to AA miles. (Indirect conversions via hotel programs tend to yield poor value.)

The AA DFW-PVG nonstop does have Avios availability in Economy, but the redemption rate is not particularly attractive:



And the OP and family would have the additional cost of getting to DFW from LAX.

(I do admit that I was surprised to see no carrier surcharge on this particular BAEC redemption.)