As a pp advised, separate it all out.
Calling, texting and coming over daily is too much. Decide with your DP what you're both comfortable with, then he sets the boundary with her. If she turns up unannounced, you don't have to let her in. You don't have to answer every call or respond to texts immediately. If she asks to come over, you can say it's not a good time/doesn't work today/let's set a date for next week.
The bags of stuff: is there anything sentimental in there at all? Some stuff might have holes but has anything been stored well? If it's just old junk, refuse it and return it to her each and every time. Again, your DP needs to set a boundary here.
Your parents. What business is it of theirs how much money/support your in-laws offer? They're behaving strangely. Why are they annoyed, unless you're repeatedly turning to them for money? My parents have been more generous than my in-laws but don't know that and have never asked to compare. Shut this down.
Money from your in-laws. Your MIL has bought an outfit as a gift, that's lovely. The lack of card or feeling of congratulations from your FIL is sad – maybe focus less on the money (your post does seem a bit entitled), and think about how your partner feels. He's just become a parent and his own parent isn't emotionally supportive. That's a much bigger issue than money.
MIL's repetitive money comments. Are you sure you're not promoting these? It seems odd she keeps mentioning it, and given the tone of your post is it perhaps the case that you're hinting at financial struggle or hinting at wanting support, maybe mentioning your parents' help and letting that information dangle, and she's trying, rightly, to shut that down?
If not, and she's just out of the blue announcing randomly "I'm not giving you money", you can say, "Yes, I know, you've mentioned this before; several times. Is there a reason you keep repeating yourself?"