Since I work in US on H1B visa, is it possible for me to cover my parents under the insurance provided by my employer?
Probably not. This is generally only available for your spouse and dependent children, and even then, you usually can't add people to your policy at any time, only during certain times of the year or at times when your circumstances change.
Is there any particular visitor insurance I can take for my mom that would cover an expense like this one?
If she has medical insurance at home that covers her abroad, certainly see what is covered. Beyond that, you aren't likely to find great options at this point. Temporary coverage for visitors certainly exists, but there's no way it could be a profitable business if it worked the way you want: you've waited until she already needs medical care to buy insurance. That's like trying to buy homeowners insurance while your house is on fire. Short-term and travel insurance policies have significant limitations and exclusions that usually preclude coverage for pre-existing conditions.
Any idea of the costs I could incur if I am not able to find an insurance to cover this?
While health care costs are high in the US, it's certainly possible to see a doctor and pay the (inflated) uninsured price. In some cases, discounts may be available for people without insurance, and you should certainly ask about that up front.
The cheapest option is likely to be a "doc-in-a-box" clinic, often staffed by a nurse practitioner, at a drug store in some states. This is likely to be under $100, but is really meant more for routine matters: infections requiring antibiotics, strep throat, a check and prescription refills for ongoing health conditions, school/employment physicals, etc... It's not where you'd want to go for a second opinion on arthritis. Urgent care facilities are staffed to a higher level and can handle more care. The cash price may be up to $200, but could increase if they run tests while you're there. Still, as the name implies, that's more for urgent (but non-emergency) situations: serious cuts requiring stitches, fractures, sudden illness, etc... It's probably not the best place for this either unless she's having an immediate flare-up and needs help.
Some general practitioners (uninsured price for a visit is likely to be under $200, but ask, and any lab tests would be separate) can treat arthritis, but a second opinion probably implies that you want a specialist, namely a rheumatologist. A specialist is likely to charge more, perhaps up to a few hundred dollars, but you can call up local rheumatologists offices, explain that your mother is uninsured and the situation, and ask what they'd charge for an office visit (they may be unable to answer). If she had lab tests back home, she could request the results and bring them.
Prescription medications, particularly brand name drugs not available as generics, can be extremely expensive in the United States. If she is prescribed any drugs for her condition, those may be absurdly unaffordable (they also may not be available back home to continue her care). Doctors often don't know how much drugs cost, but that's something to discuss with the doctor if medication is prescribed as well as ensuring that she'll be able to continue taking it when she goes home.
