With visa refusals, there is no point re-applying unless you are able to change the part of your application (or its supporting documents) that got you refused in the first place, or else you will face the same result.
However it is entirely possible that you can be successful when re-applying if you give the ECO what they want.
Looking at the images of the refusal notice you have provided, it's very clear why you have been refused. For your next application, make sure the include the following:
- Be consistent in your purpose for the trip. You can't say you wish to visit your son when you will only be spending a few hours with them. Whether or not he visits you later in India is completely irrelevant. If you are going to visit your son, make sure you are visiting him for a significant portion of your trip, otherwise do not mention it as your main reason, instead:
- Write and submit a travel itinerary. It does not have to be super specific, just what you plan to do each day.
- Give more details about your son, and ask him to write you an invitation/sponsor letter. Mention if he is a British citizen, and if not, under what premise he is residing in the UK. Mention his job/occupation. Read this answer if you want to know more about what he should include in his invitation letter.
- If someone is financially sponsoring you, they need to write a letter that explains to the ECO why and how they will be doing this, in addition to the bank statements that you have provided, for example, she could mention that you have been eager to visit the UK for quite some time, and that since she supports you financially and wants you to enjoy yourself, she will be providing you with X GBP that she has been saving for a while for this purpose, perhaps have your daughter mention that paying for your trip is her way of giving back to you for all the support you gave her during her studies.
Being refused a visa is frustrating and upsetting, but you must understand the fault lies with you, and there are clear and defined things you can change to improve your next application, which can be successful.
Good luck for next time.
To expand on CMaster's point about paragraph V4.2 (Appendix V, Immigration Rules), which states the following:
Genuine intention to visit
V 4.2 The applicant must satisfy the decision maker that they are a genuine visitor. This means that the applicant:
(a) will leave the UK at the end of their visit; and
(b) will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home; and
(c) is genuinely seeking entry for a purpose that is permitted by the visitor routes (these are listed in Appendices 3, 4 and 5); and
(d) will not undertake any prohibited activities set out in V 4.5 – V 4.10; and
(e) must have sufficient funds to cover all reasonable costs in relation to their visit without working or accessing public funds. This includes the cost of the return or onward journey, any costs relating to dependants, and the cost of planned activities such as private medical treatment.
For point (a): You need to prove that there is something compelling that will make you leave the UK at the end of your visit and return home. To this end, mentioning that you will 'only spend a few hours' with your son probably did not help. Things you can show to prove you will return home include (but are not limited to): family dependents, a job, property/asset ownership. Try and prove these to increase your chances.
For point (b): Is related to (a), but not the same, it has more to do with people making multiple visit visa applications within a short persion of time, which would lead the ECO to believe you plan on spending most of your time in the UK. I have no reason why CMaster or the ECO would suspect you of falling under this category unless you've made multiple visits to the UK in the recent past.
For point (c): This means that the ECO needs to be satisfied that the reason you are actually coming to the UK for is the same as the reason you say you are coming to the UK. To convince the ECO of this, you will need to give a strong 'main purpose' of your trip, and stick to it in your itinerary.
For point (d): As long as you avoid acting suspicious, and maintain consistency in your application, this should be fine.
For point (e): This has to do with your daughter sponsoring you, and frankly, I think the weakest point in your application. Your daughter is spending most of her entire savings on this trip for you. You either need to (with her) come up with a really compelling reason as to why she is spending 90% of her savings on you, or either find another sponsor, or show that your daughter actually has more savings than just £3,000. My suggestion would be to say that:
- You've been planning this trip for a very long time
- You will be shopping in the UK and bringing stuff back for your daughter (which would help justify why she is giving you so much money)
- She is repaying you for your kindness and support during her studies
Now keep in mind, the refusal letter does say that any future applications you make will be considered on their individual merits, however I'm fairly certain that there's a possibility they will look at previous applications made and see if you're changing your application falsely simply to get a visa (just a hunch, no proof for this), so be careful not to alter your application in such a way that seems suspicious.
Also remember, even if you change everything to what you believe is perfect, it is entirely possible that you will get refused again due to the reason I spoke of in the previous paragraph, or different reasons entirely. It is completely up to you to decide whether is is worth the effort and money to make another application.
I hope I've helped. (Please keep in mind, however, that I am not an ECO, IO or immigration specialist. If you would like professional advice, please contact a solicitor! It will prevent bad immigration history and personal stress and grief.)