Suggestions on my Itinerary

Open to suggestions and tweaks please. Still working on a solid plan. Planning to visit UK end of May!

We are a family of 4:

Day 1: land in LHR 1500hrs and reach abnb near Vauxhall bridge 1900hrs. Relax and dinner. Day 2 and Day 3: Sightseeing places in London including London eye, tower bridge, sea aquarium, guard change ceremony, etc. Day 4: start 0700am, rent a car from LHR, and drive the day to Edinburgh. Plan to stop at York. And then plan to reach Edinburgh around 1900hrs same day. Relax and dinner. Day 5 and Day 6: explore in and around Edinburgh. Couple of places in mind. Please recommend any must visits that shouldn’t be missed!!! Day 7: Start 0600am, drive and reach Manchester 10:30am, (about 5 hour drive) check out old trafford stadium tour planning to book 11:30am tour. Start driving south to Birmingham (2hr drive), reach around 1800hrs. Stay overnight. Day 8: start 0700am, reach London (3hour drive) about noon. Chill in London. Day 9: fly out of LHR 0900am

Please feel free to give me more suggestions, we are traveling from USA and wondering if this itinerary is too much of a squeeze!

Edit 1: JUST WANT TO SAY YOU ALL ARE AWESOME.