Reapplying for UK visitor visa after inadvertent overstay [closed]

My wife (a senior Indian citizen) and I (a retired air commodore) had a 10-year visitor's visa to the UK. Our son is a high-earning British citizen who sponsored us. My wife travels to the UK and the USA often as she has to look after small grandchildren in the UK (sons) and in the USA (daughters).

She had a return ticket from New Delhi to London from 15 August 17 to 22 March 18, i.e. more than six months. On arrival at London she was asked by Immigration about it, and why she would be staying in UK beyond a period of six months, the maximum allowed. She replied that she planned to visit her daughter in the USA for 3-4 months with a 10-year USA visa.

Immigration asked her to furnish proof of the air tickets. She didn't have the air tickets as her son purchases them for her in the UK. A similar case occurred earlier and the dates clearly showed in her passport. But the officer was not convinced and told her to go back to India. However they gave her a grace period of two weeks to stay with her son/grandson but cancelled her 10-year visitor's visa.

On September 1, 2017 we both travelled to the USA and stayed with our daughter and returned on February 19, 2018. The dates are there in her passport. This just goes to prove that she often goes to the USA to look after her small grandson there. As such she fully planned to go to the USA after about 2 months in the UK. Spend 3-4 months in the USA, return to th UK and depart on March 22, 2018, without overstaying the six-month limit.

She now (March 9, 2018) wants to reapply for a six-month visitor or have her 10-year visitor's visa reinstated, to be with her young grandson. Will her six-month visitor's visa, or reinstatement of her 10-year visitor's visa, be accepted considering the circumstances mentioned above?