100 options isn't exactly a lot...
This is usually the process in brokered options:...
Large volumes usually trade with a delta hedge attached.... that's because if an OTC broker is working 10.000 options, it will likely take some time. So a MM will give a price, based on a reference price in the underlying. Say, INTC ref 54.80, May 55 call - 0.75@0.85 for 2.5k size.
Than the broker can work that market and get it tighter.. to say 0.77@.83 for 5k, 2 or 3 MMs. Then their client can come in ... Seller for 15k @0.78... MMs respond by plucking it off, or staying put @0.77... Broker might get a desk at a bank involved to built the size... see who's interested.
If it starts trading, because someone says "buy @0.78 for 5k"... then the rest usually follows.
When that trade is basically done, you agree on the delta, with the reference price still at 54.80... so say delta of 48. Options go through, either during hrs or after hrs.. and the stock hedge will follow on the back-end at clearing level... you usually don't see that stock volume on-exchange. If the current spot is off the reference, the delta (obviously) can make a big difference...If the current spot is way off the reference... dollars... , you could re-price the entire thing... sometimes it busts. Sometimes you don't re-price and if you're a buyer you might make extra money on the trade since you would gain on the gamma.
These MMs are all the usual suspects. They quote OTC in size (like in my example) and the quote on-screen.. in lesser size... either minimum required, or bigger if the edge is larger. The reason they quote in smaller size on-screen is because they have the added risk of delta exposure. This is the reason your order of 100 lots is broken up in several executions.
If they get filled at their bid, they still need to do their hedge.... then, depending on the size they got hit, they might move the underlying spot somewhat initially... and that could be a reason your 100 lots might not get filled fully...
You can't access a MM directly, because they don't have clients. And they don't trade directly with retail, since there need to be all sorts of agreements in place regarding settlement and fees etc. And also, 100 lots isn't really a lot... they are quite busy (usually) being on the phone with OTC brokers and banks etc working many thousands of options... no time for a 100 lot.