Well, frankly, I don't think Beckett needs to PROVE she loves Castle, so that would be my first issue. Secondly, I think if she didn't have some kind of anger she wouldn't be Beckett. However, I think the anger will be more about lack of trust and Castle's sheer stupidity in digging into her mom's murder and putting HIMSELF at risk. I think there will be a bit of foreshadowing in the upcoming episode with Slaughter. (Love that name!) If Castle needs to SEE that Beckett loves him (which is different than PROVE) I think her concern and upset over him putting his own life in danger would bring that out. However, the idea of her going, "It's okay Dear, I understand" would IMO be a total cop-out and very OCC.
The other thing is Beckett has already been working with letting go of her mom's murder, or at least not making it a priority over having a relationship. When presented with the information from Rick that they would kill her if she kept digging it's possible she will BE in a place where letting go will feel doable. However, I think because of Rick's digging and the things coming up on the case they are on it may be too late to avoid that trigger.
Wouldn't it be ironic that Castle WITHHOLDING the information is what causes the problem. IE, had Kate known about the deal to keep her alive she might have steered AWAY from the stuff on this case that brought up her mom's murder or handed it off to someone else, telling Gates because it could potentially be about her Mother she should be off of it (thereby going full circle from the top of the season when Gates told her she would never let an officer investigate their own shooting.) In fact, what if Katye does just that, WITHOUT, knowing about the deal but because of her own therapy work? Then Castle would feel safe in telling her, but also have the whole issue of trust brought up, plus that of his own safety.