Labour economics, Instrumental Variables

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Hi, I am working on a paper to find the relationship between hiring a live-in domestic helper(DH) and  labour force participation(LFP) of mother. It is believed the DH will subsitute the child-care work of mother.
So the equation I want to estimate is LFP= a + b (DH) + controls
Both LFP and DH are binary varables.
DH is endgenous so that I have to use IV and estiamte by 2sls. The instrument I use is "the presence of the 4th room at home" to proxy the presence of DH. I restrict the sample to women with 3 & 4 rooms at home only.
The first-stage regression shows that the IV is valid.
Some concerns over the endogeneity of the IV have been noticed, for example women will move to lareger houses intentionally to hire a domestic helper.
Also the larger houses may imply more unobserved wealth.
May I ask if there are any more concerns about this IV? And what robust test should I use to test it in order to deplete the concern?  

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关键词：instrumental Instrument Variables Economics Economic instrument domestic equation presence between

How to define DH in your sample? Is DH same to ILO's domestic worker? Why is DH endogenous? To my humble opinion, including DH directly  in the traditional wage and supply 2sls is fine.