First of all… CONGRATULATIONS !!
Sounds like you had a Wedding that was more in tune with what you both needed at this time.
Your MIL is probably embarassed because you TOLD everyone previously about your Wedding Plans, and sent out the Save the Dates.
Some would say you broke a Rule of Etiquette, in that you told everyone, and then you changed your mind.
I would not be one of those people… because according to the strictest Rules of Etiquette, Save the Dates, ARE NOT AN INVITE. They are just a curtesy form of a “heads up”
You are right, it is YOUR WEDDING (especially seeing as you were the guys paying for it) so you can do it however you see fit. For you guys, and your situation that was Eloping. Period
And so if that had been your choice, and you had actually sent out the REAL INVITES, then you would have sent out a follow-up annoucement that noted that the formal wedding was off.
That is how things go… are done.
On the otherhand, now that you are married, if you wanted to throw some sort of a Party (Open House) or a Back-Home Reception you could still … something simple like Cake & Champagne… or even more elaborate like Nibbles & Cocktails – or if you have the finances, a meal (be it something casual like a Backyard BBQ or full-on fussy like a sit-down Dinner).
OR you could have a more fancy event sometime later on down the road (when you have the money needed) to mark an Anniversary Celebration, or a Vow Renewal (1, 3, 5, 10+ Years from now… the choice again is yours)
As for your MIL… try to be nice, afterall she is your Hubby’s Mom (and will be pretty much forever)… BUT she sooo needs to get over HER ISSUES
You guys are adults, and can do as you please… her grown son doesn’t belong to her, or need to bow to her whims and wishes (bear this part in mind, because it could be an issue in future encounters with her)… He needs to sit her down and set the record straight… this was not YOUR CHOICE, it was something that the TWO OF YOU agreed on, and did together.