Since you are travelling with kids, the easiest place to connect on the 6th would be PIT.
LAX-PIT UA458 940A-517P
PIT-CLE UA4810 707P-802P

Alternatively, look at PHX
LAX-PHX UA6526 750A-1009A
PHX-CLE UA1297 1215P-603P

Yes, you would have some regional equipment, but both are very easy places to do online UA connections. PIT has very few pax since US dehubbed it; there is also a Mr. Rodgers display.

The PHX option is nice as you would have a PMCO crew and plane, which IMHO are nicer than the PMUA.