Well, my standard reply to SS was always, "ask your father," so if your partner won't back up your parenting of the boys, then leave it all to her. (I didn't want to be SS's parent, it wasn't my job and my DH did it fine on his own.)

She should be backing you up.  When the kid comes to her to ask the same thing.  "stepdad already told you no.. you got your answer from us".

Disengaging also is an option.  Step back and let her parent.  If you have issues with things the kids are doing.. go to her with it.  Don't pick up after them..or get after them.  You can say things like "I noticed a lot of urine on the floor in the bathroom.. looks like the boys need you to help them remember their bathroom manners"..or  "the I saw lots of crumbs in the living room.. can you remind the boy no eating inthere?

I am going to make the assumption that the boys are with their father the week they aren't with you. I think that could be hard for them. Think about how you would feel living in two different places. It is a balancing act for you and the boys. For now because they are so young let their Mum handle things. If they do things that bother you talk with her about trying to make things better for you.She is the parent.

Does your SO have rules and boundaries in place with her children? Does she give them chores and hold them accountable when they don't do them? Does she punish the children if they are not behaving or doing what they are told when they are told?
Or does she allow the children to run over her and act completely helpless and bewildered as to why her children act the way they do? Does she allow them to call the shots and do whatever they want while she stands by wringing her hands?

You might have a Disney parent on your hand if you answered more yes to the second set of questions. In that instance all you can do is disengage and let her know she is the parent and needs to step up and start parenting. Don't allow her to manipulate you into raising her children for her because it's too hard for her.

I never tried to parent my step children. If they deferred a problem to me I would tell them "your Dad is the boss" ask him. 
They did not visit very often as their mother had a myriad of excuses as to why they couldn't.

I must admit they were pretty well behaved. If they did the wrong thing both their bio parents would be pretty quick to pull them up. One did complain to me once that her mother had hit her. My son who is considerably older overheard and asked why she had not done what she had been requested to do before it got to that. 

They are young but still mold-able at their ages. I am assuming that you had not lived together prior to this new house? If that is the case it makes sense for his behavior but does not excuse it.

He is trying to test waters and see where he fits in to this new life his mom now has with you. He also has an active father, so there is sometimes a sense that he would be betraying his relationship with his dad if he gets too close to you.

I agree with the others who said that you need to let his mom be the primary parent. You just be her back up. Take on more of the "fun uncle" role. Do the cool stuff and let their mom deal with the actual parenting. 

As someone who is a total type A personality, trust me, I know this is hard!! But once the dust settles, he understands you aren't taking his dad's place, his mom still loves him and he has a place in your home- hopefully things will go back to normal. 

I do want to add, that even in taking a parenting step back, do not allow blatant disrespect. As a step parent I fully believe that our only job is to show our stepkids basic common courtesy and kindness. Our stepkids owe is the same common courtesy and respect as an adult in the home.