It doesn’t matter who writes the invitation. You both can invite the parents. Gor a TRV the parents savings are what is important not the child in Canada. They should include the family finances in Canada in the application as well. You can invite someone on a TRV or a supervisa while on a TRV. For a supervisa the other spouse can co-sponsor.
Nope. If the invitees total income does not meet the minimum required income for their family + parents, there are ineligible to sponsor anyone to Canada. In that case it totally depends on parents income back home. Unless OPs in-laws family is well off it will be little difficult to show enough finances for parents to get a TRV approval.
I would recommend the following:
1. Both you and your wife can invite her parents to Canada on a TRV.
2. Just mention that they are visiting her daughter and their son-in-law. No need to mention your spouse pregnancy to avoid complications.
3. You write a letter of sponsorship based on your annual income and get it notarized in your province of residence, and attach it with the TRV application. In the letter of sponsorship, mention that you are taking their responsibility and you will make sure they will go back to India after visiting your family.
4. If you have any bank balance in Canada, get a letter from the back stating that you have x dollars in the account and the account was opened on x date etc.
5. Print out the monthly transaction statement of your bank account to show that you have not deposited funds recently and that you have a stable source of savings to support your family and visitors (In case of unexpected lay off from job etc).
6. Your in-laws should show their financial statements from India to prove that they are capable or at least partially capable of funding their trip.
7. Financial documents of your in-laws will also help in establishing significant ties to India.
What you are trying to show the VO is that you have enough funds to support two visitors to Canada and your in-laws also have enough funds to support their travel to Canada. Your sponsorship and funds will add a lot of weight to their application and the chances of TRV rejection will be very very low.
By doing all the above, you are presenting a very strong case to the VO for the TRV approval.