When you say "not enough money", what do you mean? that SHE doesn't have enough money or the game saying that YOU don't have enough money to click the option to help her?
I did some test myself and being in a relationship with Rick before starting one with me doesn't block the conversation with Thomas, probably because they are two separate things (same thing with Toren and Ogren, you can reject Thomas and still have NTR with those two). I encouraged Rick to go for Kate, I let them build a relationship, and basically follow the WT to cuck Rick and didn't have any problems with Thomas, doing the same thing I described before.
Then I try something similar to you, I started a relationship with Kate (behind Rick's back and keeping it a secret), I threw the mini game ("I'm not in the mood") and didn't choose to help her up until the point where Thomas started to fuck Kate. I thought this way, the option for the room wouldn't trigger since Thomas already have what he wanted, but I threw another minigame and the option to help her was still there, including "Put an end to this", I chose that and the next day Thomas offer me the room. Although, there is something weird about doing this in this order, if I
reject his offer, they will keep having sex "behind my back" and I can't join them, so something is probably broken doing this things in certain orders, or maybe choosing the NTR option ("Im not the mood") locks Kate in that route and "overwrites" rejecting his offer later, I don't know.
In any case, what exactly do you want? I mean, what combination are you looking for?