Don't waste time/money on cleaning the cooler lines, it is extremely unlikely that will have any effect!
Do take it someplace else to get the codes read and recorded for you accurately. Be sure to specify that it needs to be scanned for "extended" codes that include the trans codes. Even if you have to pay for such a scan, none of the FLAPS in your vicinity will/can do it for free, it will be a far better use of your time/money than fussing with the cooler lines. Like BP said, "P1870" gets set for nearly any hiccup of the trans; we are expecting that, at least. Yes, the codes you reported have nothing to do with the trans...