I wanted to add a few things:
1. OP - I can see how your SIL interpreted your text about some people not needing things the way she did. I know you didn't mean it that way, and it wasn't a horrible thing to say, but I was wincing a bit when I was reading it about how it could be interpreted. Your sentiment of SIL being family regardless of gifts is lovely. I'm not shocked given the situation that it was misinterpreted. Nothing you can do about it now other than apologize (which you have) and perhaps reassure SIL you do consider her family. Sounds like she's going through a rough time.
2. I think it's important for the terms of loans to be discussed. I borrowed a significant amount of money (five figures to give a rough idea - lower side of 5 figures) from my parents about a year ago to pay off credit card debt (interest was killing me). It was always intended (spelled out in a contract) that I would pay them back slowly - the point was to get rid of the interest and pay off every month going forward. My parents in no way expect me to never buy anything fun or to not buy gifts (I have given them and others gifts since borrowing money). They do expect me to be living within my means and would probably be concerned if I suddenly started getting people $400 gifts or something. It sounds like the situations are different - I only got one loan, but it is good to talk about the terms of the loan (when to pay back, payment plan, priority of paying it back, etc). That's really between OP's mom and brother and SIL though. I can see how it would be awkward to receive gifts if Mom is also complaining about not being paid back. Frankly, I'd be uncomfortable knowing the details of a loan to my sibling (I know some about a loan to my sister because I'm an attorney and they had me draw up a contract - but I don't know details about if/how it was paid back, etc).
3. At this point a lot has happened and there are a lot of hurt feelings. I think trying to smooth things over in a little bit when feelings have had a chance to recover is a good idea. OP, does SIL live near you? Can you make an effort to do some activities with her? Give her some support?