There's some data here about the comparative success rates of home insemination with frozen sperm versus IUI in a clinic: www.thespermbankofca.org/content/insemination-methods-outcomes

Generally, I would say that home insemination with frozen sperm is slightly cheaper and more convenient, but you trade that for the monitoring and other medical support which a clinic would provide, meaning your chances are a good bit lower per cycle. The timing is also a really significant factor when trying to conceive with frozen sperm, and this can be quite stressful to manage on your own. It's really easy to mess it up, and that's a lot of money down the drain.

You haven't said how old you are/how old your children are, and this may also influence your thinking - the fact that you became pregnancy quickly in the past is encouraging, but unfortunately doesn't guarantee that you will do so again. I would generally recommend that anyone looking to spend money on sperm first have a fertility MOT with a clinic to check for any factors which may impede conception, because it would suck to spend lots of money on attempts and only later discover that there's some reason they couldn't ever have worked.

Best of luck!