I guess it's too late now, but for the record, I still contend this bill is an unconstitutional violation of the right of each chamber to determine its own methods of proceeding, as per Sections 2(iii) and 3(iv) of Article III.
Finally, I would question the constitutionality of enacting this as a provision of federal Law rather than as an amendment to the Senate Rules. Under Article III, both Houses have the exclusive right to determine their own methods of proceeding; this bill amounts to the executive and the Senate mandating that the House conduct business in a certain way (and from the opposite perspective, the executive and the House mandating that the Senate conduct business in a certain way). I don't think any of these provisions would be inoperable as part of the House/Senate rules (I'd argue an expulsion provision would be on firmer constitutional ground in that context), but the distinction is important.
As I see it, the Constitution gives each House the power to determine their own methods of proceeding—independent of any other authority. If this bill were to become Law, however, the Senate would no longer be able to decide to meet on Discord without the House passing and the president signing a repeal bill. Basically, the president and one house of Congress would be preventing the other from deciding where and how to go about their business—which rather undermines the constitutional provision that the Senate alone make that decision.
Section 3 is definitely unconstitutional
