Dryer vent hose not staying connected to the dryer vent even with clamp

I would not do this for exactly the reasons you've asked about:

1) By sharing the bathroom vent pipe, you're ensuring that at least half the gunk that's being spewed onto your porch is going to be spewed into your bathroom unless you can find and install some kind of one-way flapper between the new "Y" fitting and the bathroom. If you do find and install such a thing, it's going to be difficult to keep clean and operational.

2) I'm assuming since you say "first floor" that you also have a second floor, in which case that's a long way to go to get up to the roof. It's not such a big deal for the bathroom fan to vent up there, but that's a long way for lint from the dryer to be carried, and it's going to be more likely to collect on the walls of the pipe over that long distance.

Do you have a crawlspace or basement that you could run a new pipe through?

If you have it too long with too many bends you will be creating a fire hazzard. You need to be able to clean out that dryer vent. If you have it running 15' one way and 10' another with 90 degree turns, then you might run into fire safty issues. If you can put it up against an outside wall, make your hole there on the second story. This will save you money, reduce fire risk greatly, and you wont have to pay a small fortune to have someone run a 30' snake to clean it every year.