Homemade tomato sauce, frozen thawed and frozen again - still good?

I have done similar types of things and lived to tell the tale. And if you knew the stuff my dad used to do you'd go grey. As long as it has been kept in the fridge and at a cold temperature I would sample it and then use it. Freezing degrades the quality of taste and texture with many things but my theory is if you heat it really well I'd eat it.

Firstly you shouldn't wait a week to freeze something since it is already old. I would discard sauce I had in the fridge for a week although it is probably safe to eat. You said you took it out for a day. Did you defrost in the fridge? IF so it was probably still mostly frozen and you could refreeze but refreezing can further degrade the quality and taste.. If you defrosted it or left it out on the counter then I wouldn't refreeze it. Tomato sauce is cheap and easy to make, I would start fresh, not worth to downside.