If she accepts the US job and moves to the US with monthly visits back to the UK, these are the potential pitfalls I can see:
- If the majority of her time is spent in the US and not living with you (nor continuously residing in the UK), she may have her ILR application refused.
- Even if she does qualify for ILR (with the justification of being abroad for work purposes, which I think is risky in this instance), she will not qualify for UK citizenship spending so much time out of the UK. If she doesn't have citizenship, you'll have to consider how to maintain her right to live/work in the UK moving forward. An important aspect of ILR is that it stands for Indefinite Leave to Remain. If you are outside the UK for 2 years, you will lose your ILR and no longer have a valid visa to live/work in the UK. It should also be emphasized that repeated short trips back to the UK do not count to maintain UK residence for ILR purposes. To maintain ILR status, you must be continuously living in the UK (general rule of thumb, less than 50% of your time should be spent outside the UK). So even if she gets ILR, if she continues to live/work in the US, her ILR could lapse after 2 years. Or during a UK visit, if an IO doesn't think she's genuinely living in the UK and has just returned for a visit to reset the 2-year clock, the IO can cancel her ILR on the spot.
There's no right or wrong decision. It's up to you, and what will be best for your situation and what your priorities and long-term goals are.