The check-in agent will see on the screen the same baggage allowance you see on your e-ticket receipt for your UA domestic ticket. Adding the onwards "dummy" segment will not change that.

Thus, you must be prepared to pay $190 to check your bags through ($40 for the second bag and $150 for the third bag). However, at worst, you pay the same amount as you would if you were not able to check your bags across the two tickets.

Thus, an issue beyond your control and which will turn out however it turns out.