It sounds like a petrol would be a better choice for the kind of driving you do. I'd expect your car to be worth around £3500 if you sell it privately (you can get a more accurate valuation here: www.honestjohn.co.uk/used-prices/). You won't get as much for it if you part-exchange, but it's a lot less hassle than having to deal with private buyers visiting your house to view the car. It depends how comfortable you are dealing with that. I'd expect a diesel Yaris that's been cared for as well as yours would be a pretty easy car to sell, so it might be worth attempting a private sale. Diesels are out of fashion at the moment, but there's definitely still a market for them.

As for its replacement, my money would go on a smaller Kia Picanto, a Honda Jazz or maybe another Yaris. If you decide to keep hold of your car, make sure your regularly drive at motorway speeds for extended periods (30 minutes plus) and you should avoid any DPF issues.