Sequential pattern mining and temporal association rule mining techniques are established techniques to mine insights into the data collected by smart home environments and ambient living systems. Local process models are a recent technique that uses constructs from the field of business process modeling to represent frequent patterns that go beyond sequential patterns and can additionally express rich ordering relations that include concurrent execution, choices, and repetition. To gain insight into the behavior within smart home environments using local process models, it is vital to focus on patterns where the activities that are described by the pattern are truly related. We show on real-life smart home data that existing techniques for mining local process models fail to do so, and address this problem by proposing novel techniques for constraint-based local process model mining, focusing on event gap constraints and time gap constraints. We observe that in order to get an accurate support count of a local process model, it is sufficient to only consider specific parts of the datasets instead of the full dataset, which allows to speed up the counting of the support of a pattern. We provide a novel algorithm to extract those relevant parts of the data for support counting. We evaluate our approach on a collection of real-life smart home data sets. We show that more insightful local process models can be mined when applying such constraints, and show the novel algorithm allows to mine them efficiently.