YTA. Having a pet is super motivating to help someone get up and around to take care of them. But that's not the problem here.

The main issue here is that you sound controlling as heck and completely apathetic to your long-term girlfriend's extremely traumatic loss. Nothing here says you support her besides financially, so no wonder she needs someone else to comfort her besides her terrible boyfriend.

You need to take a real long look at yourself as a human because at this point, I'm convinced you don't have feelings for anyone else other than yourself, and I feel so hard for your girlfriend and hope she can find the support she really needs to get her through these times. Because that''s clearly not coming from you.