OP yes, this place is very quick on the beat-up; why I avoided it until my offspring were 16 and 12 frankly. I have chosen to skip the beat ups and only respond if I can positively, so my tongue is half chewed off!
The fact that you are actually choosing to be engaged and making the effort to be present - a real effort, not lip service - will be noted by your children. You clearly have enough respect for them at this young age not to blag the 'interest' and make lame excuses will be noted by them (and their friends believe it or not!). Parenting is sacrificial: self interest dies for the greater good, and that comes in many expressions - even giving up the 'ideal' 50/50, which is debatable!
My children know that my Ex made a different choice to you, and now don't have the closeness I had sought for them, and when it suits them not to see him, I now allow that choice (at 14 I stopped pressing him).
Despite DexH having every opportunity to arrange his work life 80% of the time and choose any week day, so long as it was regular and consistent (I bench marked a guide of 70% as being consistent enough to have value and not be harmful for the mental health as we all have to deal with disappointment sometimes) the frequency weekly, twice weekly, alternate weeks complete flexibility and proximity not an issue as school equidistant, and given he could arrange his golf diary and make 100% tee-times, and Fridays - members days - around his work schedule, I failed miserably to secure face-time with him.
At the age of 5 my son unfortunately, learned the reality of someone choosing 'self 'consistently over him (and his younger sister). This continued and for 14 months, and only 9 mid-week visits coming to fruition, dealing with the consistent cancellations, I admitted defeat.
When my lawyer cautioned me that his lawyer had made it clear that if I persisted in texting on a Monday to find out what day that week worked best for him and a reminder on Wednesday, I would be charged with harassment. So, I ceased with the vain hope of mid week contact. I had long given up the idea of a consistent day, and would take any day he would offer contact for the sake of my son, then almost 7 and DD 3.
My ex worked for himself, had a good team around him and he found the time for golf, so one might think he could have carved out time for the children he apparently desperately wanted (3 unsuccessful rounds of IVF with W2. I'm W3, no overlap with w2). Weekend contact at this stage was either a saturday or sunday every week and was at best, 3 out of 5 weekends, and occasionally 3 weeks in a row no show. (he left when DD was 5 months old and son barely 4, hence weekly contact, not fortnightly).
So,you can't change your hours, you work in a highly scheduled profession, with little scope for flexibility. Legitimate reasons. Your children will understand these constraints and have less of a difficult time reconciling that reality than a choice of not being able to be as present as you would like, than mine have where a little white ball had greater value. Playing off +2 isn't an excuse, and as a HC 9, I get the addiction-ish.
I think you are right to see the value in your children having time with invested GP's and Mummy over the ideology of 50/50 and child minder... They will thank you for that, I assure you. Any mother worth her salt would ask a Judge to query if this was in the children's best interest. When my ex wanted our 8month old daughter to spend overnights with him, rather than drive her the arduous 3 mile journey on Saturday at 4,5 or 6pm, (located 27 miles outside of London so a 25 min round trip, not an hour or two of solid traffic), the Judge asked DexH how he felt taking a 5 month old breast-fed baby away from an additional 3-4 feeds would be in DD's best interests? He didn't have an answer. I shall never forget the sarcasm of his reply "appeal only if you grow a pair of functioning mammary glands or there is a significant uplift in travel time, let's say 45 minutes each way". My son continued to stay over-night, but my daughter was returned.
If you are present through texts or send small cute notes or cards to your daughter when she has significant (to her) events at school, and you can't be there, make sure she has something to hold onto so she KNOWS you noticed she was doing something and you really do wish you could be there. Your exW will be thrilled that her daughter feels not forgotten. She may even send you a recording of the parent teacher interview, the concert, the games match, or salient minutes and your daughter will be thrilled that you saw it at all. Yes, 5 mins to buy a card, 5 mins to write and stick on a stamp, and I can testify to the figurative fact that her heart will swell 5 times in size when she reads the card, sees the text, reads the email that were your job more flexible, you WOULD choose to be there - if you could. Buy a couple of books of ten stamps and a couple of packs of notelets and keep a few at work and at home, even in the car. Go to the pound shop or Claires accessories and split up a pack of hair clips, stickers or funky sticky mini notes or something to pop in occasionally... When my daughter started boarding recently, we made up a thing called 'monimals'. animals that come from the imagination as my art skills are crap. Draw her something. The time you want to be with her expressed in other ways and face time her builds memories and connection.
They want to know and have tangible evidence of being important to you - they see through feint praise, worthless words and absent actions and then won't trust you when it matters. These things have immense value - as does showing up when you could be doing something else more fun. Parenting: where selfish ambition dies to the greater good, especially when you aren't in your first choice place, and it isn't about an equal split, it is about being, doing and showing whenever you can.
You will, because you choose too and that is wonderful.