Trinity face Catalans Dragons in the south of France tonight and were scheduled to follow that up with a clash against Salford Red Devils on Monday.
However, their fixture with Salford has been postponed due to positive cases of Covid-19 at the Red Devils, representing the second time this year a game has been postponed between the clubs because of positive tests at Salford.
Chester feels Wakefield are being pushed from "pillar to post" and admits he will be disappointed if Trinity are expected to fulfill the rearranged game in a midweek slot.
Wakefield will travel to Catalans with just 17 fit players available and have had to call upon some of their academy players to help fulfill fixtures this year.
Under the RFL Covid-19 protocols, a team can apply to postpone a match if seven or more senior players are unavailable as a result of Covid-19, either through positive tests or as close contacts.
Numerous Super League games have been postponed and even cancelled in recent weeks and Chester believes clubs without academy systems are benefitting from postponements, as they are not required to field younger players in order to fulfill matches.
"First and foremost, I will be disappointed if we are asked to play a midweek game through no fault of our own," said Chester.
"Twice, we have had games called off against Salford. The first one, what happened was inexcusable but that is for a later day.
"We have another game that gets called off and then we could be expected to play a midweek game between a Sunday and a Sunday game or a Friday and a Sunday game.
"We are getting punished and, for me, the teams that don't run an academy system are benefitting from what is happening.
"I just find it mind-blowing at times. We are doing our best to make sure we are fulfilling everything we need to.
"The St Helens game earlier this month, we brought it forward as we thought it was the right thing to do. We were due to play Sunday but they requested a Friday game with it being the Challenge Cup the following weekend
"But what kind of thanks do we get? We just get kicked from pillar to post. Through no fault of ours, we are expected to catch up on a game.
"It is just really, really frustrating.
"All we can focus on is making sure we have our own house in order and make sure we are doing the right things. Something has got to change with it."
On what needs to change to reduce the number of postponements in Super League at the moment, Chester is not so sure.
He continued: "If this was a normal season and you couldn't fulfill a game, you would have your points deducted or it would be a 24-0 loss.
"Why can't that still be the case? We are going to run out of time to get all the fixtures in.
"Something has got to change, I don't know what that is, it is far beyond my paygrade but I am sick to death of clubs like ours getting punished, or what feels like a punishment, for other clubs not following protocols or not having an academy and not being able to fulfill a fixture list."
Wakefield are 11th in the Super League table as they prepare to take on league leaders Catalans, who have lost just one of their 14 league games this year.
The Dragons emerged victorious when the sides met earlier in the season at Belle Vue and Chester has hailed the job done by Hull-born coach Steve McNamara.
"Their spine has been excellent and they have some big blokes in there that cause teams a lot of problems just with their sheer size," said Chester.
"They have got some speed on the edges. Steve McNamara has done a fantastic job there, it has taken two to three years and some investment but that is starting to come to fruition now.
"It is going to be a really physical challenge and a really big test for us but it is one the guys are looking forward to."
Former NRL half-back James Maloney is set to feature for Catalans tonight after returning from suspension while Wakefield will be without key forward Joe Westerman as he completes the Covid-19 seven-day return-to-play protocol.
"I think Maloney has been the best Australian signing we have had over here for a number of years," added Chester.
"The way he gets the team around the park and listening to him on the pitch, he has had that leadership and that is what marquee money brings you."