First of all, we always appreciate and thankful for giving us this game. Our real life is always takes priority above all and we definitely understand that, you should not be very sorry about prioritizing yourself.
As software engineer at work, there are times you have to pushback timelines but all you have to do is keep everyone updated / informed - which you already doing but try to lessen the apology part. This is your project, give timeline that will not pressure / beat you and very workable on your end.
Keep your head up and hope things get a lot better on your end. Cheers!