Oh, that's a tough one, but honestly, if it were me, I would skip Oban and Loch Lomond, and visit both Mull and the Outer Hebrides. They are wonderful and I would be hard put to choose between them, although I do have a special place in my heart for Mull (and Tobermory). Oban is really more of a jumping-off place, in my opinion and Loch Lomond is a pretty lake, but not much more.
Tobermory is charming and there is a lot you can see and do there. If you want a quick look, check out this article showing 30 of Britain's greatest villages (recently posted by JC here on the forum), and scroll down to Tobermory. https://www.telegraph.co.uk/gift/ba8bd346b29a369c
I stayed 4 nights in one of the harbor B&Bs and parked in one of the free car lots on the harbor. It's lovely to be able to walk down through the shops and restaurants that line the harbor. Bring your camera as it's very photogenic. You can visit the Isle of Mull Cheese Shop (Sgriob-ruadh Farm), which is about a mile from the harbor. There are self-guided tours to meet the farm animals and learn about traditional cheese making. There is also a cafe and a farm shop.
Also, there is a short walk from the harbor car park along the wooded hillside to Aros Park with woodland trails, a lochan and really nice waterfalls. A walk from the other end of Main Street leads along a coastal path to the Rubha Nan Gall Lighthouse. There are amazing views out over the Sound of Mull. And another short walk up the hill towards Baliscate leads to the Baliscate Standing Stones. Nearby is the site of the Baliscate Chapel, the subject of a BBC archaeology dig.
You also might want to stop at Isle of Mull Pottery, which is just beautiful. They sell some in the shops along the harbor but the main shop is in the town up above Main St. (you will pass it if you go to Calgary).
The Tobermory Bakery is wonderful—definitely stop here for one of their delectable pastries, take-away sandwiches and coffee or tea. Their Millionaire's Shortbread is incredible! There is a shop at the end of the harbor that is farthest from the ferry terminal that sells handmade chocolate with a tea room, and along the way are some very nice gift shops - I bought half my souvenirs in Mull (and I'm picky about stuff like that). Lots of nice restaurants, too. There is also a catch-and-release aquarium right on the harbor that your kids would probably love!
Don't miss Calgary Beach, which is about a 30+ minute drive—probably more like 40—from Tobermory. It's very narrow and the single track roads run through the mountains with some switchbacks, so you will need to go slow through much of it. It's well worth a visit to see the beautiful beach.
Of course, there is the Isle of Iona, the birthplace of Christianity in Scotland and filled with so much history. It makes for a wonderful day trip from Tobermory. You can drive to Fionnphort, then take the 10 minute ferry over to Iona, see the ruins and the history there, have some lunch, walk on the beach. It's an amazing day.
The Outer Hebrides are also pretty wonderful as well. I have only been to Harris and Lewis, but it was so worth a visit. Harris has the most beautiful beaches in Scotland, along with many quaint coastal villages, and Lewis is filled with incredible Neolithic sites, dramatic coastlines, fishing villages, and Lews Castle (which holds some of the famous historic Welsh Chessmen). I really loved my stay here and hope to get back there in the near future.
Edit: You could easily spend 4 nights in each place, then make your way to Edinburgh for a final 3-4 nights before returning to London. With regards to your 2nd choice, I like the Lake District and enjoyed Liverpool, but neither can compare to Mull and the Outer Hebrides.