Get your taxes done using TurboTax

"I can't find a place to indicate that the adult child is part of the family plan. "

There is no such place, because she doesn't need to indicate that her son is on her plan. It is sufficient to indicate that she has Family coverage in her HDHP.

Since I can't see your return, I can't say for sure, but I suspect what happened is that she contributed her $7,000 for her Family plan, and you contributed $3,500 for your Self plan, and you two are getting an excess contribution message for $3,500. This is not her overcontribution, it's yours.

The problem - and this is a common misunderstanding - is that a married couple with one spouse under Family HDHP coverage shares the Family coverage. That is, you don't get to contribute to your HSA independently of your spouse; instead, you two share this $7,000 contribution limit, split any way you like.

As the IRS says in Pub 969, if either spouse has Family HDHP coverage, then both spouses are considered to have Family coverage, and they share the Family contribution limit.

To fix this situation, you should do the following:

1. Tell TurboTax that you will withdraw the excess by April 15th (I hope there is enough cash to do it).

2. TurboTax will ask you who made the excess contribution - you get to pick who pays, or if you don't have enough cash in one HSA, you can withdraw parts of the excess from both HSAs.

3. Call the HSA custodian(s) before April 15th and tell them that you want to request a "withdrawal of excess contributions" (use this exact phrase).

4. The amount of the excess has been automatically added to Other Income on Schedule 1 (1040), but this is OK, because the HSA custodian is sending you a check for that amount.

5. Early next year, you will receive a 1099-SA reporting the earnings on the excess while it was in your HSA; the distribution code will be '2'. Enter that on your 2020 tax return, and the issue will be taken care of.

If this is not your situation, then come back and tell us.