Marion Blakely is hiding out on the Groundbreak in The Outer Worlds and has paid a group of thugs called The Gardeners to keep anyone from bothering her. They will not let you approach her residence, but there are a couple of ways you can deal with this issue, depending on how you like to play the game.
When you are talking to the main guard, you can offer him a bribe, as long as you have the money, or if you have a high enough Lie stat you will be able to pretend that Blakely is actually your mother, and you are there to visit her. You will need a very high Lie stat, so even if you have been focusing on Dialogue when you level up, this may not be possible for you.
If you are more of a sneaky player, then stop talking to the guard and wait for them to stop paying attention to you. Sneak over to the left side of the room and climb up the ladder near the entrance. You will need to be very careful at the top of the ladder, as it enters a short tunnel that leads to a room with a human guard and two canids. The guard and one of the canids are facing away from you, and the other canid is asleep, so if you are confident in your ability to sneak, then this is the option for you.
The final way to get through the room is to simply murder absolutely everyone inside. Once you get inside, head down to the lab itself. Here you will find two drones patrolling a hall. It doesn’t matter how you go in, those drones will attack you, so take them both out, loot the rooms on either side of the hall and take the elevator at the end.
The next room has robot enemies and drones, and when you take them all out you can head for the next room, where you will find Blakeslee. She won’t be particularly mad at you, no matter how you got inside, and if you talk to her she will give you the details you need to get into the Spacer’s Choice facility. It is also possible to intimidate her if your stats are high enough, which will get you an access code from a door inside the facility that will make getting to her office easier.