It depends
My prediction: If this the first time she has ever been in the US for more than 6 months in one calendar year, she will get told not to spend so much time here in the future and then get admitted for 6 months. You are Indian, so in all likelihood it is not even close to her first time spending this much time in the US in a year.
If they look back and see 2,3,4 years or more of 7-8 months or more in the US in each calendar year, in all likelihood her stay will get limited with annotations to advise against CIS granting extensions or adjustment of status later. If she is extremely old or shows up in a wheel chair, the chances are miniscule of her actually getting kicked out because the old INS always had an unofficial policy of not being too harsh on old people and exercising discretion to their benefit whenever possible. But she does stand a fairly good chance of getting her stay limited. Unless, of course, you work for Microsoft and live in Seattle, WA, in which case they flexed some political muscle so that all the parents of their H1Bs and L1s get to live here ilegally and indefinitely on visitor's visas.
According to you Mom is going home in June and then getting invited back for 3 months in the summer. Since June, July, and August are the main three months of the SUmmer and you said you want to invite her for three months this SUmmer, my interpretation of this is she will depart in June and return to the US within a few weeks or maybe even a few days to ask for another 3 months in the US. If that is the case she is even more likely to be pulled aside since departing for an extremely short time period after spending months and months here and then coming right back to ask for months and months more will always raise a red flag. This of course increases the likelihood that her stay will get limited. As I said, if she is particularly old, wrinked, travels in a wheel chair, or has any serious physical infirmities, it is unlikely that she will be sent packing. However, there is a fair chance if what I said has been correct that you will not get to spend as much time with Mom this summer as you planned.
Sounds to me like you want Mom to live with you, which is perfectly understandable and reasonable. What you need to do is stop circumventing the law by having her do it on visitors' documents and go about it the right way by either adjusting status or sponsoring her for an immigrant visa so she's legit and good to go when she arrives at the airport. This way you don't have to worry about her being detained by big, bad, mean immigration officers.
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Oh, wait, sorry, I forgot. Like most older Indians, after she receives a valid greencard she will switch from coming here for 4-6 months twice per year on a visitor's visa to staying in India 11 months and 3 weeks at a time and coming here for exactly 1 week per year to keep her greencard active.
