I have zero issues with donor conception (I'm a single woman currently 16 weeks pregnant after double-donor IVF) but I think you're going to need to get your head around what you're planning to tell people.
The thinking nowadays on what's best for donor-conceived children is that ideally they should know about their origins from a very early age; so early that they never have some big revelatory moment but have just always known (in an age-appropriate way) about being donor conceived. In practice, this means that other people close to you are going to end up knowing something about the situation, too - not that you'll necessarily want or need to tell absolutely everyone, but it's probably going to come up from time to time. As a minimum, I would suggest you might want to tell family something along the lines of "I decided to have another baby and I'm very happy about it".
This is an area where it sounds as though people close to you are likely to have (and vocally express) strong opinions about your decisions, so I would really recommend working through your feelings on the issues involved before you proceed. You could look at getting some counselling from someone specialising in fertility matters; also you might find the Donor Conception Network really helpful.
In terms of your older children, are they old enough to have a conversation with about possibly having another sibling? Would you be swayed by their opinions? It sounds as though you have worries about how they might feel, so I guess I'm wondering whether it makes sense to explore that with them to help inform your thinking.
One other thing I would note is that, if you're planning on using a donor through an informal arrangement (i.e. outside a clinic), this can be legally very complicated. Many people have conceived in this way and it can work really well, but I would always advise caution as it can be a real minefield. So, make sure you do your homework!
Best of luck, whatever you decide.