First of all, have you made lodging accommodations anywhere along your route? Are you all individuals, or are you two married couples? I ask because if you're travelling as four separate people, you're probably going to need two twin bedded rooms, unless someone in your group has a need for privacy, in which case it might be one twin and two singles. Twin bedded rooms are a bit harder to come by, especially on Skye.
If this is your first visit, then you need to determine who will be doing the driving, and if that person is comfortable driving a car with standard transmission. You can hire a car with automatic transmission to make things a little bit easier. It will cost just a little bit more. Also, if you're planning to do a lot in Glasgow, and then drive on to Oban, you need to get a really early start out of Edinburgh.
On your visit to Glasgow, please make sure that you have plenty of one and two pound coins for the parking meters, if you decide to street park. I don't remember whether the parking meters take credit cards. I don't know which part of the Glasgow School of Art you're planning to visit, but some of the main buildings were badly damaged by fire in 2014 and 2018, and are not yet open. You may want to check that out before you pay to park nearby. There are several parking garages in central Glasgow - there should be ones close to your destinations. Best to check that out before you go. Glasgow is fairly easy to negotiate by car, but you have to watch out for bus lanes and bike lanes.
Just a warning - the Kelvingrove Art Gallery is huge! Plan on spending three to four hours minimum, especially if you're planning to tour the new Linda McCartney exhibit.
Oban is about a three hour drive from the west end of Glasgow. Make sure to give yourselves enough time for a leisurely drive.
Oban to Mallaig can conceivably be done in three hours, but that would be no fun for anyone. The A830 is one of the most scenic main roads in Scotland. Best to give yourselves four to 4 1/2 hours, especially as you have to be at the ferry slip at least 30 minutes prior to sailing. Be sure to make reservations for the Mallaig to Armadale ferry, and for your lodging on Skye.
Day seven is going to involve a lot of driving, but Eilean Donan and part of Loch Ness are on your way to Inverness. You're probably going to be stopping for sightseeing and photos along the way, so don't try to make Culloden by the end of the day if you're going to be exhausted. The visitor centre closes at 7 p.m. in June, although you can still wander the battlefield until dusk. You really need a good two hours to get an appreciation for the site, especially if you're planning to see the exhibits in the visitor centre.
Unless you have a pressing need to get back to Edinburgh at an early hour on day 8, you could visit Culloden on the morning of that day. Inverness to Stirling is the better part of three hours, longer if you stop on the way. The Kelpies don't necessarily have to take a long time to visit, and Falkirk is very close to Edinburgh.
Your itinerary is busy, but not frantic! As it's your first time over, you're going to want to see as much as possible. But if it gets to be too much, cut back where you can, and save the rest for your next visit. And there will be a next visit. Holidays in Scotland are like potato chips - you can't have just one! If more than one of you is willing to drive, that would make it a bit easier for everyone. I'd advise against doing a Rabbie's tour, as it doesn't appear that it would work with the way you have arranged your route.
Best wishes for your travels. You'll have plenty of daylight in June!