I think if you are driving that the Islands , whilst absolutely beautiful would probably be a bit much for a first trip .
If you are driving from England , I think you should perhaps look as others have suggested at the borders / Dumfries and Galloway .I think you will also need to factor in driving time ie how many hours with breaks would you be comfortable driving for without having to factor in an overnight stay ? As the options available for this may not be suitable for your children e.g busy hotels , premier inns etc ( dependent on budget too ).
I think you would need to look at fishing lodges / rural estates and then check out how many cottages etc are on site . There may be a few , but may be quite far apart from each other , have a lot of privacy - so that may work for you .
You will also need to consider budget , are you flexible for dates etc ?
I use cottages.com , air bnb a lot for family holidays . There are lots of filters re dates , budget etc . Had a quick look on Airbnb and there are filters re waterfront .
For the hot tub , this isn’t something I have searched for , but would usually be available in more luxurious accom where they are catering for couples on breaks .
I have had some great family holidays , staying on farms and private rural estates in cottages . Would probably have been close to rivers for fishing , but not “on site “ and no hot tubs .But if you are able to push your budget , you may get this offered in the luxury cottages etc .
I would try searching for luxurious fishing lodges and then try and check which ones would offer you the privacy you need and the hot tub.
You could also post in scotsnet to see if you get any more suggestions . Good luck and hope you all have a fab holiday when it comes .