I would not recommend using a stop order at the open for options, especially at the open.
Because options are 'derivative' contracts, they are based on the price of the underlying. Only after the underlying exchanges have opened, do the options exchanges open. And usually then, only a few market participants will actually participate in the opening rotation - usually those that have to, such as Primary market makers.
The view of market makers is that participating at the open is risky - there can be a lot of wild swings in the underlying as people send in large orders in the underlying, which may in turn cause changes in price.
During liquid trading conditions, in-the-money options typically follow the price of the underlying, but are still subject to the maximum spread ($5.00) with each option being for 100 shares. Your stop-loss could go off, but at $5.00 below what it is worth, or $500 per options contract.
During illiquid trading conditions (e.g. immediately after or at the open), the market maker may not be there at all, you could get executed at significantly worse prices. People have been executed at $0.01 in the past...
If you sell an option for cheaper than what is someone willing to pay, does [your broker] sell it for the best price or for the price you chose to sell it?
Brokers are obliged to follow the National Best Bid or Offer (NBBO). Executing a trade outside of the NBBO is called a trade-through, and a prohibited practice.
I'm trying to figure out if I can do stop loss on in-the-money options.
Most brokerage platforms may allow you to send in such an order. That does not mean that doing so is wise.
all I'm trying to do is sell for the best price right when the trading session begins in the morning.
I would suggest instead to figure out what the option is worth, and submit the order, gradually decreasing the price using a limit order. Looking at historical market data, you may be able to see when the spread is narrowest (difference between the bid and offer), and determine the times typically after the open that the market is most competitive.
If it is urgent, use a marketable order (i.e. the price of the order to sell is lower than the best bid on the market). At least you can set the worst price your order could get traded.