Regardless of your opinion on the hierarchy of the relationships, and regardless of glib sayings, the fact remains that this man is her son, as well as your husband. The way people will refer to others depends on context and the subject of the sentence. Do you expect people to refer to this man as "her daughter-in-law's husband"?
I think you are being unreasonable. Parents are perfectly entitled to give gifts to their married offspring without addressing it to their spouse too. If your husband wants to share the monetary gift with you - either by giving you exactly half, or putting the money towards a joint purchase, that is between you and him.
Unless your own parents spent $1000 on the celebratory dinner for you both, I don't think the two gifts are equivalent. Honestly, in your shoes, I'd just think how generous my mother-in-law had been and be delighted that I'd probably benefit by proxy.
You've said you've had a decent relationship with your MIL until now, so saying you'll be acting much cooler towards her in future after she has just given her own son a very generous gift reflects very badly on you. It makes you sound petty and spiteful. If she'd had a long history of excluding you and this was simply the final hurtful straw it might be different, but it doesn't sound like this at all.
I'd also be concerned about the fact that, based on this thread at least, you seem to lack any identity of your own and see yourself as an extension of your husband. It's not healthy, especially not in the long term.
You are clearly an accomplished woman - you have a PhD. You got that on your own merit. You did the research, you wrote your thesis and defended it. But you're insisting that it's a joint achievement rather than both of you achieving something at the same time. Your husband did his own PhD. Even if you're in a STEM field and your PhDs are on a subset of the same large project, they have to be distinct or else they miss the originality element to be PhDs. Couples should support each other, and it's great that you have a close and supportive relationship, but your achievements are your own.
You must see this, surely? Your research profile will be based on your work, not his?
Sincerely, I congratulate you on your graduation. But I think your reaction to a generous gift from your mother-in-law to her son is unreasonable.