I think it's horrid, Pingu...having just read the first few posts...
I know it's your baby's right to see her dad but it must be shockingly painful for you to have to 'share' her with this other woman.
When we have children we do so knowing we will share them with their father - someone we know and trust.
If the partner then lets us down, leaves, lies to us etc. it feels like sharing your child with a stranger, because it isn't the person you thought you knew - and who in their right mind hands their baby over to a stranger? I think this should be a huge factor in the way these things are managed - the mothers feelings are seldom taken into account, which means the person with most care is often stressed, unhappy and angry - hardly a good thing for her children.
I am struggling with the same issues to a degree, but have been extremely lucky in that my child's dad has left us alone for a few years. I imagine that if your ex is using his contact to make himself look good, it will be shortlived. If he really cares about your daughter, he will be consistent and a good person for her to know.
Some blokes don't care enough to be consistent, but still try to save their reputation by getting access and misusing it, being unreliable and hurting their kids' feelings. I think this is very wrong.
I hope your daughter's dad is one of the decent ones, in which case you will learn to relax and be pleased that he is in touch with her.
Another huge issue is the fact that these are OUR children - we wipe their bottoms every day, we know them inside out - we are there for them Someone (father or not) swanning in once a week and acting like they have some kind of right, some ownership of a child they see for 10 percent of its life - is infuriating, and I can't stand it personally.
When ds1's dad used to visit, I was always angry about the fact he barely knew my child - ds1 was about a year old then. I insisted on coming with him and his older kids when they took ds into town. He hated me being there despite the fact he'd never lived with us, didn't understand ds's needs or words...and had lied to me about a lot of things. He wouldn't even let me know his address or number. He said whee they were going once, I followed 10 mins later to give him ds's hat, and he wasn't there
The next week his ex wife rang and told me he was living with someone else. For all I knew he was taking ds there. I flipped, lost it with him, asked for a few weeks break to calm down. He never rang again.
He couldn't understand my protectiveness toward my baby, inasmuch as I wanted to know where he was taking him...
I later heard that the new woman was horrid to his other children, so was glad I didn't let ds go and see her.
Sorry not much help, just sharing.